1
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Zeng Y, Zhou B, Chen S. Exact zeros of fidelity in finite-size systems as a signature for probing quantum phase transitions. Phys Rev E 2024; 109:064130. [PMID: 39021006 DOI: 10.1103/physreve.109.064130] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2023] [Accepted: 05/24/2024] [Indexed: 07/20/2024]
Abstract
The fidelity is widely used to detect quantum phase transitions, which is characterized by either a sharp change of fidelity or the divergence of fidelity susceptibility in the thermodynamical limit when the phase-driving parameter is across the transition point. In this work, we unveil that the occurrence of exact zeros of fidelity in finite-size systems can be applied to detect quantum phase transitions. In general, the fidelity F(γ,γ[over ̃]) always approaches zero in the thermodynamical limit, due to the Anderson orthogonality catastrophe, no matter whether the parameters of two ground states (γ and γ[over ̃]) are in the same phase or different phases, and this makes it difficult to distinguish whether an exact zero of fidelity exists by finite-size analysis. To overcome the influence of orthogonality catastrophe, we study finite-size systems with twist boundary conditions, which can be introduced by applying a magnetic flux, and demonstrate that exact zeros of fidelity can be always accessed by tuning the magnetic flux when γ and γ[over ̃] belong to different phases. On the other hand, no exact zero of fidelity can be observed if γ and γ[over ̃] are in the same phase. We demonstrate the applicability of our theoretical scheme by studying concrete examples, including the Su-Schrieffer-Heeger model, Creutz model, and Haldane model. Our work provides a practicable way to detect quantum phase transitions via the calculation of fidelity of finite-size systems.
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2
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Nian YH, Vinograd I, Green T, Chaffey C, Massat P, Singh RRP, Zic MP, Fisher IR, Curro NJ. Spin Echo, Fidelity, and the Quantum Critical Fan in TmVO_{4}. PHYSICAL REVIEW LETTERS 2024; 132:216502. [PMID: 38856271 DOI: 10.1103/physrevlett.132.216502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/26/2023] [Revised: 10/16/2023] [Accepted: 04/22/2024] [Indexed: 06/11/2024]
Abstract
Using spin-echo nuclear magnetic resonance in the model transverse field Ising system TmVO_{4}, we show that low frequency quantum fluctuations at the quantum critical point have a very different effect on ^{51}V nuclear spins than classical low-frequency noise or fluctuations that arise at a finite temperature critical point. Spin echoes filter out the low-frequency classical noise but not the quantum fluctuations. This allows us to directly visualize the quantum critical fan and demonstrate the persistence of quantum fluctuations at the critical coupling strength in TmVO_{4} to high temperatures in an experiment that remains transparent to finite temperature classical phase transitions. These results show that while dynamical decoupling schemes can be quite effective in eliminating classical noise in a qubit, a quantum critical environment may lead to rapid entanglement and decoherence.
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Affiliation(s)
- Y-H Nian
- Department of Physics and Astronomy, University of California Davis, Davis, California, USA
| | - I Vinograd
- Department of Physics and Astronomy, University of California Davis, Davis, California, USA
| | - T Green
- Department of Physics and Astronomy, University of California Davis, Davis, California, USA
| | - C Chaffey
- Department of Physics and Astronomy, University of California Davis, Davis, California, USA
| | - P Massat
- Geballe Laboratory for Advanced Materials and Department of Applied Physics, Stanford University, California 94305, USA
| | - R R P Singh
- Department of Physics and Astronomy, University of California Davis, Davis, California, USA
| | - M P Zic
- Geballe Laboratory for Advanced Materials and Department of Physics, Stanford University, California 94305, USA
| | - I R Fisher
- Geballe Laboratory for Advanced Materials and Department of Applied Physics, Stanford University, California 94305, USA
| | - N J Curro
- Department of Physics and Astronomy, University of California Davis, Davis, California, USA
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3
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Upadhyay AK, Sasihithlu K. Tunability in 3-Site Electronic Excitation Transfer Dynamics: Insights into the Role of Perturbative Coupling. J Phys Chem B 2024; 128:4047-4052. [PMID: 38652834 DOI: 10.1021/acs.jpcb.3c07968] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/25/2024]
Abstract
Electronic excitation transfer dynamics in photosynthetic systems, including the Fenna-Matthews-Olson complex, are often modeled using the interaction picture of three two-level systems, also known as the 3-site system. Among the two possible configurations, uphill and downhill, a recent publication reported an intriguing correlation between population dynamics and the intersite coupling. Specifically, the uphill configuration has been shown to have a pronounced dependence on perturbations in the intersite coupling, whereas the downhill configuration displays negligible dependence. In this study, we consider a generic 3-site configuration and model site interactions through the Markovian master equation. Through this approach, we derive succinct analytical expressions for the population dynamics between the sites, shedding light on the differences in behavior between the two configurations. Using these analytical expressions, we demonstrate the range of tunability in population dynamics achievable with minimal changes in intersite coupling, and we validate these findings through simulation results. These insights into the population dynamics of a 3-site system are expected to play a crucial role in facilitating the design of efficient energy-transfer pathways in molecular systems.
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Affiliation(s)
- Amit Kumar Upadhyay
- Department of Energy Science and Engineering, Indian Institute of Technology Bombay, Mumbai 400076, India
| | - Karthik Sasihithlu
- Department of Energy Science and Engineering, Indian Institute of Technology Bombay, Mumbai 400076, India
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4
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Fei Z, Ma YH. Temperature fluctuations in mesoscopic systems. Phys Rev E 2024; 109:044101. [PMID: 38755872 DOI: 10.1103/physreve.109.044101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2023] [Accepted: 02/26/2024] [Indexed: 05/18/2024]
Abstract
Temperature is a fundamental concept in thermodynamics. In macroscopic thermodynamics, systems possess their own intrinsic temperature which equals the reservoir temperature when they equilibrate. In stochastic thermodynamics for simple systems at the microscopic level, thermodynamic quantities other than temperature (a deterministic parameter of the reservoir) are stochastic. To bridge the disparity in the perspectives about temperature between the micro- and macroregimes, we assign a generic mesoscopic N-body system an intrinsic fluctuating temperature T in this work. We simplify the complicated dynamics of numerous particles to one stochastic differential equation with respect to T, where the noise term accounts for finite-size effects arising from random energy transfer between the system and the reservoir. Our analysis reveals that these fluctuations make the extensive quantities (in the thermodynamic limit) deviate from being extensive. Moreover, we derive finite-size corrections, characterized by heat capacity of the system, to the Jarzynski equality. A possible violation of the principle of maximum work that scales with N^{-1} is also discussed. Additionally, we examine the impact of temperature fluctuations in a finite-size Carnot engine. We show that irreversible entropy production resulting from the temperature fluctuations of the working substance diminishes the average efficiency of the cycle as η_{C}-〈η〉∼N^{-1}, highlighting the unattainability of the Carnot efficiency η_{C} for mesoscopic heat engines even under the quasistatic limit. Our general framework paves the way for further exploration of nonequilibrium thermodynamics and the corresponding finite-size effects in a mesoscopic regime.
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Affiliation(s)
- Zhaoyu Fei
- Department of Physics and Key Laboratory of Optical Field Manipulation of Zhejiang Province, Zhejiang Sci-Tech University, Hangzhou 310018, China
- Graduate School of China Academy of Engineering Physics, No. 10 Xibeiwang East Road, Haidian District, Beijing 100193, China
| | - Yu-Han Ma
- Graduate School of China Academy of Engineering Physics, No. 10 Xibeiwang East Road, Haidian District, Beijing 100193, China
- Department of Physics, Beijing Normal University, Beijing 100875, China
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5
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Lim LK, Lou C, Tian C. Mesoscopic fluctuations in entanglement dynamics. Nat Commun 2024; 15:1775. [PMID: 38413673 PMCID: PMC10899636 DOI: 10.1038/s41467-024-46078-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2023] [Accepted: 02/12/2024] [Indexed: 02/29/2024] Open
Abstract
Understanding fluctuation phenomena plays a dominant role in the development of many-body physics. The time evolution of entanglement is essential to a broad range of subjects in many-body physics, ranging from exotic quantum matter to quantum thermalization. Stemming from various dynamical processes of information, fluctuations in entanglement evolution differ conceptually from out-of-equilibrium fluctuations of traditional physical quantities. Their studies remain elusive. Here we uncover an emergent random structure in the evolution of the many-body wavefunction in two classes of integrable-either interacting or noninteracting-lattice models. It gives rise to out-of-equilibrium entanglement fluctuations which fall into the paradigm of mesoscopic fluctuations of wave interference origin. Specifically, the entanglement entropy variance obeys a universal scaling law in each class, and the full distribution displays a sub-Gaussian upper and a sub-Gamma lower tail. These statistics are independent of both the system's microscopic details and the choice of entanglement probes, and broaden the class of mesoscopic universalities. They have practical implications for controlling entanglement in mesoscopic devices.
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Affiliation(s)
- Lih-King Lim
- School of Physics, Zhejiang University, 310027, Hangzhou, Zhejiang, China
| | - Cunzhong Lou
- School of Physics, Zhejiang University, 310027, Hangzhou, Zhejiang, China
| | - Chushun Tian
- CAS Key Laboratory of Theoretical Physics and Institute of Theoretical Physics, Chinese Academy of Sciences, 100190, Beijing, China.
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6
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Jiang Y, Wen R, Zhang Y. Exact quench dynamics from algebraic geometry. Phys Rev E 2023; 108:024128. [PMID: 37723800 DOI: 10.1103/physreve.108.024128] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2021] [Accepted: 07/12/2023] [Indexed: 09/20/2023]
Abstract
We develop a systematic approach to compute physical observables of integrable spin chains with finite length. Our method is based on the Bethe ansatz solution of the integrable spin chain and computational algebraic geometry. The final results are analytic and no longer depend on Bethe roots. The computation is purely algebraic and does not rely on further assumptions or numerics. This method can be applied to compute a broad family of physical quantities in integrable quantum spin chains. We demonstrate the power of the method by computing two important quantities in quench dynamics-the diagonal entropy and the Loschmidt echo-and obtain analytic results.
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Affiliation(s)
- Yunfeng Jiang
- Shing-Tung Yau Center and School of Physics, Southeast University, Nanjing 210096, China
| | - Rui Wen
- Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, British Columbia, Canada V6T 1Z1
| | - Yang Zhang
- Interdisciplinary Center for Theoretical Study, University of Science and Technology of China, Hefei, Anhui 230026, China
- Peng Huanwu Center for Fundamental Theory, Hefei, Anhui 230026, China
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7
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Khalouf-Rivera J, Gamito J, Pérez-Bernal F, Arias JM, Pérez-Fernández P. Excited-state quantum phase transitions in the anharmonic Lipkin-Meshkov-Glick model: Dynamical aspects. Phys Rev E 2023; 107:064134. [PMID: 37464676 DOI: 10.1103/physreve.107.064134] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2023] [Accepted: 06/07/2023] [Indexed: 07/20/2023]
Abstract
The standard Lipkin-Meshkov-Glick (LMG) model undergoes a second-order ground-state quantum phase transition (QPT) and an excited-state quantum phase transition (ESQPT). The inclusion of an anharmonic term in the LMG Hamiltonian gives rise to a second ESQPT that alters the static properties of the model [Gamito et al., Phys. Rev. E 106, 044125 (2022)2470-004510.1103/PhysRevE.106.044125]. In the present work, the dynamical implications associated to this new ESQPT are analyzed. For that purpose, a quantum quench protocol is defined on the system Hamiltonian that takes an initial state, usually the ground state, into a complex excited state that evolves on time. The impact of the new ESQPT on the time evolution of the survival probability and the local density of states after the quantum quench, as well as on the Loschmidt echoes and the microcanonical out-of-time-order correlator (OTOC) are discussed. The anharmonity-induced ESQPT, despite having a different physical origin, has dynamical consequences similar to those observed in the ESQPT already present in the standard LMG model.
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Affiliation(s)
- J Khalouf-Rivera
- Departamento de Física Aplicada III, Escuela Técnica Superior de Ingeniería, Universidad de Sevilla, 41092 Sevilla, Spain
- Departamento de Ciencias Integradas y Centro de Estudios Avanzados en Física, Matemáticas y Computación, Universidad de Huelva, Huelva 21071, Spain
| | - J Gamito
- Departamento de Física Atómica, Molecular y Nuclear, Facultad de Física, Universidad de Sevilla, Apartado 1065, E-41080 Sevilla, Spain
| | - F Pérez-Bernal
- Departamento de Ciencias Integradas y Centro de Estudios Avanzados en Física, Matemáticas y Computación, Universidad de Huelva, Huelva 21071, Spain
- Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Fuentenueva s/n, 18071 Granada, Spain
| | - J M Arias
- Departamento de Física Atómica, Molecular y Nuclear, Facultad de Física, Universidad de Sevilla, Apartado 1065, E-41080 Sevilla, Spain
- Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Fuentenueva s/n, 18071 Granada, Spain
| | - P Pérez-Fernández
- Departamento de Física Aplicada III, Escuela Técnica Superior de Ingeniería, Universidad de Sevilla, 41092 Sevilla, Spain
- Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Fuentenueva s/n, 18071 Granada, Spain
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8
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Franchi A, Pelissetto A, Vicari E. Quantum critical behaviors and decoherence of weakly coupled quantum Ising models within an isolated global system. Phys Rev E 2023; 107:014113. [PMID: 36797878 DOI: 10.1103/physreve.107.014113] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/20/2022] [Accepted: 12/23/2022] [Indexed: 06/18/2023]
Abstract
We discuss the quantum dynamics of an isolated composite system consisting of weakly interacting many-body subsystems. We focus on one of the subsystems, S, and study the dependence of its quantum correlations and decoherence rate on the state of the weakly-coupled complementary part E, which represents the environment. As a theoretical laboratory, we consider a composite system made of two stacked quantum Ising chains, locally and homogeneously weakly coupled. One of the chains is identified with the subsystem S under scrutiny, and the other one with the environment E. We investigate the behavior of S at equilibrium, when the global system is in its ground state, and under out-of-equilibrium conditions, when the global system evolves unitarily after a quench of the coupling between S and E. When S develops quantum critical correlations in the weak-coupling regime, the associated scaling behavior crucially depends on the quantum state of E, whether it is characterized by short-range correlations (analogous to those characterizing disordered phases in closed systems), algebraically decaying correlations (typical of critical systems), or long-range correlations (typical of magnetized ordered phases). In particular, different scaling behaviors, depending on the state of E, are observed for the decoherence of the subsystem S, as demonstrated by the different power-law divergences of the decoherence susceptibility that quantifies the sensitivity of the coherence to the interaction with E.
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Affiliation(s)
- Alessio Franchi
- Dipartimento di Fisica dell'Università di Pisa and INFN, Largo Pontecorvo 3, I-56127 Pisa, Italy
| | - Andrea Pelissetto
- Dipartimento di Fisica dell'Università di Roma Sapienza and INFN Sezione di Roma I, I-00185 Roma, Italy
| | - Ettore Vicari
- Dipartimento di Fisica dell'Università di Pisa and INFN, Largo Pontecorvo 3, I-56127 Pisa, Italy
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9
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Quantum Speed-Up Induced by the Quantum Phase Transition in a Nonlinear Dicke Model with Two Impurity Qubits. Symmetry (Basel) 2022. [DOI: 10.3390/sym14122653] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Abstract
In this paper, we investigate the effect of the Dicke quantum phase transition on the speed of evolution of the system dynamics. At the phase transition point, the symmetry associated with the system parity operator begins to break down. By comparing the magnitudes of the two types of quantum speed limit times, we find that the quantum speed limit time of the system is described by one of the quantum speed limit times, whether in the normal or superradiant phase. We find that, in the normal phase, the strength of the coupling between the optical field and the atoms has little effect on the dynamical evolution speed of the system. However, in the superradiant phase, a stronger atom–photon coupling strength can accelerate the system dynamics’ evolution. Finally, we investigate the effect of the entanglement of the initial state of the system on the speed of evolution of the system dynamics. We find that in the normal phase, the entanglement of the initial state of the system has almost no effect on the system dynamics’ evolution speed. However, in the superradiant phase, larger entanglement of the system can accelerate the evolution of the system dynamics. Furthermore, we verify the above conclusions by the actual evolution of the system.
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10
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Sudden quench of harmonically trapped mass-imbalanced fermions. Sci Rep 2022; 12:19710. [PMID: 36385321 PMCID: PMC9668996 DOI: 10.1038/s41598-022-24228-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2022] [Accepted: 11/11/2022] [Indexed: 11/17/2022] Open
Abstract
Dynamical properties of two-component mass-imbalanced few-fermion systems confined in a one-dimensional harmonic trap following a sudden quench of interactions are studied. It is assumed that initially the system is prepared in the non-interacting ground state and then, after a sudden quench of interactions, the unitary evolution is governed by interacting many-body Hamiltonian. By careful analysis of the evolution of the Loschmidt echo, density distributions of the components, and entanglement entropy between them, the role of mass imbalance and particle number imbalance on the system's evolution stability are investigated. All the quantities studied manifest a dramatic dependence on the number of heavy and lighter fermions in each component at a given quench strength. The results may have implications for upcoming experiments on fermionic mixtures with a well-defined and small number of particles.
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11
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Gong H, Wang Y, Zheng X, Xu RX, Yan Y. Nonequilibrium work distributions in quantum impurity system-bath mixing processes. J Chem Phys 2022; 157:054109. [DOI: 10.1063/5.0095549] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The fluctuation theorem, where the central quantity is the work distribution, is an important characterization of nonequilibrium thermodynamics. In this work, based on the dissipaton-equation-of-motion theory, we develop an exact method to evaluate the work distributions in quantum impurity system-bath mixing processes, in the presence of non-Markovian and strong couplings. Our results not only precisely reproduce the Jarzynski equality and Crooks relation, but also reveal rich information on large deviation. The numerical demonstrations are carried out with a spin-boson model system.
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Affiliation(s)
- Hong Gong
- University of Science and Technology of China, China
| | - Yao Wang
- Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, China
| | - Xiao Zheng
- Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, China
| | - Rui-Xue Xu
- University of Science and Technology of China, China
| | - YiJing Yan
- Department of Chemical Physics, USTC, China
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12
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Numerical renormalization group study of the Loschmidt echo in Kondo systems. Sci Rep 2022; 12:9799. [PMID: 35697737 PMCID: PMC9192593 DOI: 10.1038/s41598-022-14108-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2022] [Accepted: 06/01/2022] [Indexed: 11/09/2022] Open
Abstract
We study the dynamical properties of the one-channel and two-channel spin-1/2 Kondo models after quenching in Hamiltonian variables. Eigen spectrum of the initial and final Hamiltonians is calculated by using the numerical renormalization group method implemented within the matrix product states formalism. We consider multiple quench protocols in the considered Kondo systems, also in the presence of external magnetic field of different intensities. The main emphasis is put on the analysis of the behavior of the Loschmidt echo L(t), which measures the ability of the system's revival to its initial state after a quench. We show that the decay of the Loschmidt echo strongly depends on the type of quench and the ground state of the system. For the one-channel Kondo model, we show that L(t) decays as, [Formula: see text], where [Formula: see text] is the Kondo temperature, while for the two-channel Kondo model, we demonstrate that the decay is slower and given by [Formula: see text]. In addition, we also determine the dynamical behavior of the impurity's magnetization, which sheds light on identification of the relevant time scales in the system's dynamics.
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13
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Franchi A, Rossini D, Vicari E. Quantum many-body spin rings coupled to ancillary spins: The sunburst quantum Ising model. Phys Rev E 2022; 105:054111. [PMID: 35706175 DOI: 10.1103/physreve.105.054111] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2022] [Accepted: 04/20/2022] [Indexed: 06/15/2023]
Abstract
We study the ground-state properties of a quantum sunburst model, composed of a quantum Ising spin ring in a transverse field, symmetrically coupled to a set of ancillary isolated qubits, to maintain a residual translation invariance and also a Z_{2} symmetry. The large-size limit is taken in two different ways: either by keeping the distance between any two neighboring ancillary qubits fixed or by fixing their number while increasing the ring size. Substantially different regimes emerge, depending on the various Hamiltonian parameters: For small energy scale δ of the ancillary subsystem and small ring-qubit interaction κ, we observe rapid and nonanalytic changes in proximity to the quantum transitions of the Ising ring, both first order and continuous, which can be carefully controlled by exploiting renormalization-group and finite-size scaling frameworks. Smoother behaviors are instead observed when keeping δ>0 fixed and in the Ising disordered phase. The effect of an increasing number n of ancillary spins turns out to scale proportionally to sqrt[n] for sufficiently large values of n.
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Affiliation(s)
- Alessio Franchi
- Dipartimento di Fisica, Università di Pisa and INFN, Largo Pontecorvo 3, 56127 Pisa, Italy
| | - Davide Rossini
- Dipartimento di Fisica, Università di Pisa and INFN, Largo Pontecorvo 3, 56127 Pisa, Italy
| | - Ettore Vicari
- Dipartimento di Fisica, Università di Pisa and INFN, Largo Pontecorvo 3, 56127 Pisa, Italy
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14
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Orthogonality catastrophe and quantum speed limit for spin chain at finite temperature. Sci Rep 2022; 12:5058. [PMID: 35322146 PMCID: PMC8943030 DOI: 10.1038/s41598-022-09010-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2021] [Accepted: 03/16/2022] [Indexed: 11/08/2022] Open
Abstract
We present an interesting relationship between the orthogonality catastrophe (OC) and the quantum speed limit (QSL) for a spin chain with uniform nearest neighbour couplings perturbed by an impurity spin. We thoroughly study the catastrophic QSL that specifies a bound on the evolution time between the initial and final states and in this respect, link it to the emerging OC effect. It is found that the speed of state evolution subtle but fundamental, and the bound characterized by QSL shows the same behaviours as the OC effect in the thermodynamic limit. It allows us to reveal some universal properties, in particular finite temperature effects. Significantly, the threshold of temperature and system size is clearly demonstrated for the QSL under finite temperature.
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15
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Shao C, Lu H, Zhang X, Yu C, Tohyama T, Lu R. High-Harmonic Generation Approaching the Quantum Critical Point of Strongly Correlated Systems. PHYSICAL REVIEW LETTERS 2022; 128:047401. [PMID: 35148147 DOI: 10.1103/physrevlett.128.047401] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2021] [Revised: 11/22/2021] [Accepted: 01/06/2022] [Indexed: 06/14/2023]
Abstract
By employing the exact diagonalization method, we investigate the high-harmonic generation (HHG) of the correlated systems under the strong laser irradiation. For the extended Hubbard model on a periodic chain, HHG close to the quantum critical point (QCP) is more significant compared to two neighboring gapped phases (i.e., charge-density-wave and spin-density wave states), especially in low frequencies. We confirm that the systems in the vicinity of the QCP are supersensitive to the external field and more optical-transition channels via excited states are responsible for HHG. This feature holds the potential of obtaining high-efficiency harmonics by making use of materials approaching QCP. Based on the two-dimensional Haldane model, we further propose that the even- or odd-order components of generated harmonics can be promisingly regarded as spectral signals to distinguish the topologically ordered phases from locally ordered ones. Our findings in this Letter pave the way to achieve ultrafast light source from HHG in strongly correlated materials and to study quantum phase transition by nonlinear optics in strong laser fields.
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Affiliation(s)
- Can Shao
- Institute of Ultrafast Optical Physics, Department of Applied Physics and MIIT Key Laboratory of Semiconductor Microstructure and Quantum Sensing, Nanjing University of Science and Technology, Nanjing 210094, China
| | - Hantao Lu
- School of Physical Science and Technology and Key Laboratory for Magnetism and Magnetic Materials of the MoE, Lanzhou University, Lanzhou 730000, China
| | - Xiao Zhang
- Institute for Theoretical Solid State Physics, Leibniz IFW Dresden, Helmholtzstr. 20, 01069 Dresden, Germany
| | - Chao Yu
- Institute of Ultrafast Optical Physics, Department of Applied Physics and MIIT Key Laboratory of Semiconductor Microstructure and Quantum Sensing, Nanjing University of Science and Technology, Nanjing 210094, China
| | - Takami Tohyama
- Department of Applied Physics, Tokyo University of Science, Tokyo 125-8585, Japan
| | - Ruifeng Lu
- Institute of Ultrafast Optical Physics, Department of Applied Physics and MIIT Key Laboratory of Semiconductor Microstructure and Quantum Sensing, Nanjing University of Science and Technology, Nanjing 210094, China
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16
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Yang S, Xu JB. Quantum entanglement and criticality in a one-dimensional deconfined quantum critical point. Phys Rev E 2021; 104:064121. [PMID: 35030944 DOI: 10.1103/physreve.104.064121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2021] [Accepted: 12/03/2021] [Indexed: 06/14/2023]
Abstract
We investigate the ground-state quantum entanglement in a one-dimensional incarnation of deconfined quantum critical point by making use of the finite-size density matrix renormalization group method. We observe two distinct behaviors of two-site entanglement calculated on odd and even bonds, and the difference O_{E} is shown to obey conventional scaling relations for order parameters. Accurate deconfined critical point and associated critical exponents are numerically extracted from finite-size scaling analyses. We further notice a close similarity between O_{E} and the valence-bond-solid order parameter and same observations are also obtained for quantum coherence and trace distance. Furthermore, the deconfined critical point is suggested to possess rich quantum entanglement other than the two-site entanglement from the residual entanglement perspective. Our work explores the critical characteristics of the one-dimensional deconfined quantum critical point from the quantum information aspect and provides insights for its ground-state entanglement structure.
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Affiliation(s)
- Sheng Yang
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Jing-Bo Xu
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027, China
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17
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Japaridze GI, Cheraghi H, Mahdavifar S. Magnetic phase diagram of a spin-1/2 XXZ chain with modulated Dzyaloshinskii-Moriya interaction. Phys Rev E 2021; 104:014134. [PMID: 34412371 DOI: 10.1103/physreve.104.014134] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2020] [Accepted: 06/29/2021] [Indexed: 11/07/2022]
Abstract
We consider the ground-state phase diagram of a one-dimensional spin-1/2 XXZ chain with a spatially modulated Dzyaloshinskii-Moriya interaction in the presence of an alternating magnetic field applied along the z[over ̂] axis. The model is studied using the continuum-limit bosonization approach and the finite system exact numerical technique. In the absence of a magnetic field, the ground-state phase diagram of the model includes, besides the ferromagnetic and gapless Luttinger-liquid phases, two gapped phases: the composite (C1) phase characterized by the coexistence of long-range-ordered (LRO) alternating dimerization and spin chirality patterns, and the composite (C2) phase characterized by, in addition to the coexisting spin dimerization and alternating chirality patterns, the presence of LRO antiferromagnetic order. In the case of mentioned composite gapped phases, and in the case of a uniform magnetic field, the commensurate-incommensurate type quantum phase transitions from a gapful phase into a gapless phase have been identified and described using the bosonization treatment and finite chain exact diagonalization studies. The upper critical magnetic field corresponding to the transition into a fully polarized state has been also determined. It has been shown that the very presence of a staggered component of the magnetic field vapes the composite (C1) in favor of the composite gapped (C2) phase.
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Affiliation(s)
- G I Japaridze
- Center for Condensed Matter Theory and Quantum Computations Ilia State University, Tbilisi, Georgia
| | - Hadi Cheraghi
- Department of Physics, University of Guilan, 41335-1914, Rasht, Iran
| | - Saeed Mahdavifar
- Department of Physics, University of Guilan, 41335-1914, Rasht, Iran
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18
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Francis A, Zhu D, Huerta Alderete C, Johri S, Xiao X, Freericks JK, Monroe C, Linke NM, Kemper AF. Many-body thermodynamics on quantum computers via partition function zeros. SCIENCE ADVANCES 2021; 7:7/34/eabf2447. [PMID: 34407938 PMCID: PMC8373169 DOI: 10.1126/sciadv.abf2447] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/14/2020] [Accepted: 06/28/2021] [Indexed: 06/13/2023]
Abstract
Partition functions are ubiquitous in physics: They are important in determining the thermodynamic properties of many-body systems and in understanding their phase transitions. As shown by Lee and Yang, analytically continuing the partition function to the complex plane allows us to obtain its zeros and thus the entire function. Moreover, the scaling and nature of these zeros can elucidate phase transitions. Here, we show how to find partition function zeros on noisy intermediate-scale trapped-ion quantum computers in a scalable manner, using the XXZ spin chain model as a prototype, and observe their transition from XY-like behavior to Ising-like behavior as a function of the anisotropy. While quantum computers cannot yet scale to the thermodynamic limit, our work provides a pathway to do so as hardware improves, allowing the future calculation of critical phenomena for systems beyond classical computing limits.
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Affiliation(s)
- Akhil Francis
- Department of Physics, North Carolina State University, Raleigh, NC 27695, USA
| | - Daiwei Zhu
- Joint Quantum Institute and Department of Physics, University of Maryland, College Park, MD 20742, USA
- Center for Quantum Information and Computer Science, University of Maryland, College Park, MD 20742, USA
| | - Cinthia Huerta Alderete
- Joint Quantum Institute and Department of Physics, University of Maryland, College Park, MD 20742, USA
- Instituto Nacional de Astrofísica, Óptica y Electrónica, Calle Luis Enrique Erro No. 1, Sta. Ma. Tonantzintla, Pue. CP 72840, Mexico
| | - Sonika Johri
- IonQ Inc., 4505 Campus Dr, College Park, MD 20740, USA
| | - Xiao Xiao
- Department of Physics, North Carolina State University, Raleigh, NC 27695, USA
| | - James K Freericks
- Department of Physics, Georgetown University, 37th and O Sts. NW, Washington, DC 20057, USA
| | - Christopher Monroe
- Joint Quantum Institute and Department of Physics, University of Maryland, College Park, MD 20742, USA
- Center for Quantum Information and Computer Science, University of Maryland, College Park, MD 20742, USA
- IonQ Inc., 4505 Campus Dr, College Park, MD 20740, USA
| | - Norbert M Linke
- Joint Quantum Institute and Department of Physics, University of Maryland, College Park, MD 20742, USA
| | - Alexander F Kemper
- Department of Physics, North Carolina State University, Raleigh, NC 27695, USA.
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19
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Mzaouali Z, Puebla R, Goold J, El Baz M, Campbell S. Work statistics and symmetry breaking in an excited-state quantum phase transition. Phys Rev E 2021; 103:032145. [PMID: 33862795 DOI: 10.1103/physreve.103.032145] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2021] [Accepted: 03/02/2021] [Indexed: 11/07/2022]
Abstract
We examine how the presence of an excited-state quantum phase transition manifests in the dynamics of a many-body system subject to a sudden quench. Focusing on the Lipkin-Meshkov-Glick model initialized in the ground state of the ferromagnetic phase, we demonstrate that the work probability distribution displays non-Gaussian behavior for quenches in the vicinity of the excited-state critical point. Furthermore, we show that the entropy of the diagonal ensemble is highly susceptible to critical regions, making it a robust and practical indicator of the associated spectral characteristics. We assess the role that symmetry breaking has on the ensuing dynamics, highlighting that its effect is only present for quenches beyond the critical point. Finally, we show that similar features persist when the system is initialized in an excited state and briefly explore the behavior for initial states in the paramagnetic phase.
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Affiliation(s)
- Zakaria Mzaouali
- ESMaR, Faculty of Sciences, Mohammed V University in Rabat, Morocco
| | - Ricardo Puebla
- Instituto de Física Fundamental, IFF-CSIC, Calle Serrano 113b, 28006 Madrid, Spain.,Centre for Theoretical Atomic, Molecular and Optical Physics, Queen's University Belfast, Belfast BT7 1NN, United Kingdom
| | - John Goold
- School of Physics, Trinity College Dublin, College Green, Dublin 2, Ireland
| | - Morad El Baz
- ESMaR, Faculty of Sciences, Mohammed V University in Rabat, Morocco
| | - Steve Campbell
- School of Physics, University College Dublin, Belfield, Dublin 4, Ireland.,Centre for Quantum Engineering, Science, and Technology, University College Dublin, Belfield, Dublin 4, Ireland
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20
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Zhang KL, Song Z. Quantum Phase Transition in a Quantum Ising Chain at Nonzero Temperatures. PHYSICAL REVIEW LETTERS 2021; 126:116401. [PMID: 33798382 DOI: 10.1103/physrevlett.126.116401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/21/2020] [Accepted: 02/22/2021] [Indexed: 06/12/2023]
Abstract
We study the response of a thermal state of an Ising chain to a nonlocal non-Hermitian perturbation, which coalesces the topological Kramer-like degeneracy in the ferromagnetic phase. The dynamic responses for initial thermal states in different quantum phases are distinct. The final state always approaches its half component with a fixed parity in the ferromagnetic phase but remains almost unchanged in the paramagnetic phase. This indicates that the phase diagram at zero temperature is completely preserved at finite temperatures. Numerical simulations for Loschmidt echoes demonstrate such dynamical behaviors in finite-size systems. In addition, it provides a clear manifestation of the bulk-boundary correspondence at nonzero temperatures. This work presents an alternative approach to understanding the quantum phase transitions of quantum spin systems at nonzero temperatures.
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Affiliation(s)
- K L Zhang
- School of Physics, Nankai University, Tianjin 300071, China
| | - Z Song
- School of Physics, Nankai University, Tianjin 300071, China
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21
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Chu Y, Zhang S, Yu B, Cai J. Dynamic Framework for Criticality-Enhanced Quantum Sensing. PHYSICAL REVIEW LETTERS 2021; 126:010502. [PMID: 33480770 DOI: 10.1103/physrevlett.126.010502] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/25/2020] [Accepted: 11/24/2020] [Indexed: 06/12/2023]
Abstract
Quantum criticality, as a fascinating quantum phenomenon, may provide significant advantages for quantum sensing. Here we propose a dynamic framework for quantum sensing with a family of Hamiltonians that undergo quantum phase transitions (QPTs). By giving the formalism of the quantum Fisher information (QFI) for quantum sensing based on critical quantum dynamics, we demonstrate its divergent feature when approaching the critical point. We illustrate the basic principle and the details of experimental implementation using quantum Rabi model. The framework is applicable to a variety of examples and does not rely on the stringent requirement for particular state preparation or adiabatic evolution. It is expected to provide a route towards the implementation of criticality-enhanced quantum sensing.
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Affiliation(s)
- Yaoming Chu
- MOE Key Laboratory of Fundamental Physical Quantities Measurements, Hubei Key Laboratory of Gravitation and Quantum Physics, School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
- International Joint Laboratory on Quantum Sensing and Quantum Metrology, Institute for Quantum Science and Engineering, Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Shaoliang Zhang
- MOE Key Laboratory of Fundamental Physical Quantities Measurements, Hubei Key Laboratory of Gravitation and Quantum Physics, School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
- International Joint Laboratory on Quantum Sensing and Quantum Metrology, Institute for Quantum Science and Engineering, Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Baiyi Yu
- MOE Key Laboratory of Fundamental Physical Quantities Measurements, Hubei Key Laboratory of Gravitation and Quantum Physics, School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
- International Joint Laboratory on Quantum Sensing and Quantum Metrology, Institute for Quantum Science and Engineering, Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Jianming Cai
- MOE Key Laboratory of Fundamental Physical Quantities Measurements, Hubei Key Laboratory of Gravitation and Quantum Physics, School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
- International Joint Laboratory on Quantum Sensing and Quantum Metrology, Institute for Quantum Science and Engineering, Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan 430074, China
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai, 200062, China
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22
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Lewis-Swan RJ, Muleady SR, Rey AM. Detecting Out-of-Time-Order Correlations via Quasiadiabatic Echoes as a Tool to Reveal Quantum Coherence in Equilibrium Quantum Phase Transitions. PHYSICAL REVIEW LETTERS 2020; 125:240605. [PMID: 33412057 DOI: 10.1103/physrevlett.125.240605] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2020] [Revised: 09/09/2020] [Accepted: 10/26/2020] [Indexed: 06/12/2023]
Abstract
We propose a new dynamical method to connect equilibrium quantum phase transitions and quantum coherence using out-of-time-order correlations (OTOCs). Adopting the iconic Lipkin-Meshkov-Glick and transverse-field Ising models as illustrative examples, we show that an abrupt change in coherence and entanglement of the ground state across a quantum phase transition is observable in the spectrum of multiple quantum coherence intensities, which are a special type of OTOC. We also develop a robust protocol to obtain the relevant OTOCs using quasi-adiabatic quenches through the ground state phase diagram. Our scheme allows for the detection of OTOCs without time reversal of coherent dynamics, making it applicable and important for a broad range of current experiments where time reversal cannot be achieved by inverting the sign of the underlying Hamiltonian.
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Affiliation(s)
- R J Lewis-Swan
- Homer L. Dodge Department of Physics and Astronomy, The University of Oklahoma, Norman, Oklahoma 73019, USA
- JILA, NIST, Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
| | - S R Muleady
- JILA, NIST, Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
| | - A M Rey
- JILA, NIST, Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
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23
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Fei Z, Quan HT. Nonequilibrium Green's Function's Approach to the Calculation of Work Statistics. PHYSICAL REVIEW LETTERS 2020; 124:240603. [PMID: 32639826 DOI: 10.1103/physrevlett.124.240603] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/22/2020] [Accepted: 05/29/2020] [Indexed: 06/11/2023]
Abstract
The calculation of work distributions in a quantum many-body system is of significant importance and also of formidable difficulty in the field of nonequilibrium quantum statistical mechanics. To solve this problem, inspired by the Schwinger-Keldysh formalism, we propose the contour-integral formulation for work statistics. Based on this contour integral, we show how to do the perturbation expansion of the characteristic function of work (CFW) and obtain the approximate expression of the CFW to the second order of the work parameter for an arbitrary system under a perturbative protocol. We also demonstrate the validity of fluctuation theorems by utilizing the Kubo-Martin-Schwinger condition. Finally, we use noninteracting identical particles in a forced harmonic potential as an example to demonstrate the powerfulness of our approach.
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Affiliation(s)
- Zhaoyu Fei
- School of Physics, Peking University, Beijing 100871, China
| | - H T Quan
- School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
- Frontiers Science Center for Nano-optoelectronics, Peking University, Beijing 100871, China
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24
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Wu N. Longitudinal magnetization dynamics in the quantum Ising ring: A Pfaffian method based on correspondence between momentum space and real space. Phys Rev E 2020; 101:042108. [PMID: 32422699 DOI: 10.1103/physreve.101.042108] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2020] [Accepted: 03/18/2020] [Indexed: 11/07/2022]
Abstract
As perhaps the most studied paradigm for a quantum phase transition, the periodic quantum Ising chain is exactly solvable via the Jordan-Wigner transformation followed by a Fourier transform that diagonalizes the model in the momentum space of spinless fermions. Although the above procedures are well-known, there remain some subtle points to be clarified regarding the correspondence between the real-space and momentum-space representations of the finite-size quantum Ising ring, especially those related to fermion parities. In this work, we establish the relationship between the two fully aligned ferromagnetic states in real space and the two degenerate momentum-space ground states of the classical Ising ring, with the former being a special case of the factorized ground states of the more general XYZ model on the frustration-free hypersurface. Based on this observation, we then provide a Pfaffian formula for calculating real-time dynamics of the parity-breaking longitudinal magnetization with the system initially prepared in one of the two ferromagnetic states and under translationally invariant drivings. The formalism is shown to be applicable to large systems with the help of online programs for the numerical computation of the Pfaffian, thus providing an efficient method to numerically study, for example, the emergence of discrete time crystals in related systems.
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Affiliation(s)
- Ning Wu
- Center for Quantum Technology Research, School of Physics, Beijing Institute of Technology, Beijing 100081, China
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25
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Fei Z, Freitas N, Cavina V, Quan HT, Esposito M. Work Statistics across a Quantum Phase Transition. PHYSICAL REVIEW LETTERS 2020; 124:170603. [PMID: 32412269 DOI: 10.1103/physrevlett.124.170603] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2020] [Accepted: 04/15/2020] [Indexed: 06/11/2023]
Abstract
We investigate the statistics of the work performed during a quench across a quantum phase transition using the adiabatic perturbation theory when the system is characterized by independent quasiparticles and the "single-excitation" approximation is assumed. It is shown that all the cumulants of work exhibit universal scaling behavior analogous to the Kibble-Zurek scaling for the average density of defects. Two kinds of transformations are considered: quenches between two gapped phases in which a critical point is traversed, and quenches that end near the critical point. In contrast to the scaling behavior of the density of defects, the scaling behavior of the cumulants of work are shown to be qualitatively different for these two kinds of quenches. However, in both cases the corresponding exponents are fully determined by the dimension of the system and the critical exponents of the transition, as in the traditional Kibble-Zurek mechanism (KZM). Thus, our study deepens our understanding about the nonequilibrium dynamics of a quantum phase transition by revealing the imprint of the KZM on the work statistics.
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Affiliation(s)
- Zhaoyu Fei
- School of Physics, Peking University, Beijing 100871, China
| | - Nahuel Freitas
- Complex Systems and Statistical Mechanics, Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg
| | - Vasco Cavina
- Complex Systems and Statistical Mechanics, Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg
| | - H T Quan
- School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
- Frontiers Science Center for Nano-optoelectronics, Peking University, Beijing, 100871, China
| | - Massimiliano Esposito
- Complex Systems and Statistical Mechanics, Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg
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26
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Fogarty T, Deffner S, Busch T, Campbell S. Orthogonality Catastrophe as a Consequence of the Quantum Speed Limit. PHYSICAL REVIEW LETTERS 2020; 124:110601. [PMID: 32242725 DOI: 10.1103/physrevlett.124.110601] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/25/2019] [Accepted: 02/18/2020] [Indexed: 06/11/2023]
Abstract
A remarkable feature of quantum many-body systems is the orthogonality catastrophe that describes their extensively growing sensitivity to local perturbations and plays an important role in condensed matter physics. Here we show that the dynamics of the orthogonality catastrophe can be fully characterized by the quantum speed limit and, more specifically, that any quenched quantum many-body system, whose variance in ground state energy scales with the system size, exhibits the orthogonality catastrophe. Our rigorous findings are demonstrated by two paradigmatic classes of many-body systems-the trapped Fermi gas and the long-range interacting Lipkin-Meshkov-Glick spin model.
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Affiliation(s)
- Thomás Fogarty
- Quantum Systems Unit, Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904-0495, Japan
| | - Sebastian Deffner
- Department of Physics, University of Maryland, Baltimore County, Baltimore, Maryland 21250, USA
| | - Thomas Busch
- Quantum Systems Unit, Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904-0495, Japan
| | - Steve Campbell
- School of Physics, University College Dublin, Belfield Dublin 4, Ireland
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27
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Cheraghi H, Mahdavifar S. Probing the Possibilities of Ergodicity in the 1D Spin-1/2 XY Chain with Quench Dynamics. Sci Rep 2020; 10:4407. [PMID: 32157113 PMCID: PMC7064509 DOI: 10.1038/s41598-020-61037-8] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/29/2019] [Accepted: 02/19/2020] [Indexed: 11/26/2022] Open
Abstract
Ergodicity sits at the heart of the connection between statistical mechanics and dynamics of a physical system. By fixing the initial state of the system into the ground state of the Hamiltonian at zero temperature and tuning a control parameter, we consider the occurrence of the ergodicity with quench dynamics in the one-dimensional (1D) spin-1/2 XY model in a transverse magnetic field. The ground-state phase diagram consists of two ferromagnetic and paramagnetic phases. It is known the magnetization in this spin system is non-ergodic. We set up two different experiments as we call them single and double quenches and test the dynamics of the magnetization along the Z-axis and the spin-spin correlation function along the X-axis which are the order parameters of the zero-temperature phases . Our exact results reveal that for single quenches at zero-temperature, the ergodicity depends on the initial state and the order parameter. In single quenches for a given order parameter, ergodicity will be observed with an ergodic-region for quenches from another phase, non-correspond to the phase of the order parameter, into itself. In addition, a quench from a ground-state phase point corresponding to the order parameter into or very close to the quantum critical point, hc = 1.0, discloses an ergodic behavior. Otherwise, for all other single quenches, the system behaves non-ergodic. Interestingly on the other setup, a double quench on a cyclic path, ergodicity is completely broken for starting from the phase corresponding to the order parameter. Otherwise, it depends on the first quenched point, and the quench time T when the model spent before a second quench in the way back which gives an ability to controlling the ergodicity in the system. Therefore, and contrary to expectations, in the mentioned model the ergodicity can be observed with probing quench dynamics at zero-temperature. Our results provide further insight into the zero-temperature dynamical behavior of quantum systems and their connections to the ergodicity phenomenon.
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Affiliation(s)
- Hadi Cheraghi
- Department of Physics, University of Guilan, 41335-1914, Rasht, Iran.
| | - Saeed Mahdavifar
- Department of Physics, University of Guilan, 41335-1914, Rasht, Iran
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28
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Xu C, Feng J, Kawamura M, Yamaji Y, Nahas Y, Prokhorenko S, Qi Y, Xiang H, Bellaiche L. Possible Kitaev Quantum Spin Liquid State in 2D Materials with S=3/2. PHYSICAL REVIEW LETTERS 2020; 124:087205. [PMID: 32167315 DOI: 10.1103/physrevlett.124.087205] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/12/2019] [Accepted: 02/07/2020] [Indexed: 06/10/2023]
Abstract
Quantum spin liquids (QSLs) form an extremely unusual magnetic state in which the spins are highly correlated and fluctuate coherently down to the lowest temperatures, but without symmetry breaking and without the formation of any static long-range-ordered magnetism. Such intriguing phenomena are not only of great fundamental relevance in themselves, but also hold promise for quantum computing and quantum information. Among different types of QSLs, the exactly solvable Kitaev model is attracting much attention, with most proposed candidate materials, e.g., RuCl_{3} and Na_{2}IrO_{3}, having an effective S=1/2 spin value. Here, via extensive first-principles-based simulations, we report the investigation of the Kitaev physics and possible Kitaev QSL state in epitaxially strained Cr-based monolayers, such as CrSiTe_{3}, that rather possess a S=3/2 spin value. Our study thus extends the playground of Kitaev physics and QSLs to 3d transition metal compounds.
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Affiliation(s)
- Changsong Xu
- Physics Department and Institute for Nanoscience and Engineering, University of Arkansas, Fayetteville, Arkansas 72701, USA
| | - Junsheng Feng
- Key Laboratory of Computational Physical Sciences (Ministry of Education), State Key Laboratory of Surface Physics, and Department of Physics, Fudan University, Shanghai 200433, People's Republic of China
- School of Physics and Materials Engineering, Hefei Normal University, Hefei 230601, People's Republic of China
| | - Mitsuaki Kawamura
- The Institute for Solid State Physics, The University of Tokyo, Kashiwa-shi, Chiba 277-8581, Japan
| | - Youhei Yamaji
- Department of Applied Physics, University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
| | - Yousra Nahas
- Physics Department and Institute for Nanoscience and Engineering, University of Arkansas, Fayetteville, Arkansas 72701, USA
| | - Sergei Prokhorenko
- Physics Department and Institute for Nanoscience and Engineering, University of Arkansas, Fayetteville, Arkansas 72701, USA
| | - Yang Qi
- Key Laboratory of Computational Physical Sciences (Ministry of Education), State Key Laboratory of Surface Physics, and Department of Physics, Fudan University, Shanghai 200433, People's Republic of China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, People's Republic of China
| | - Hongjun Xiang
- Key Laboratory of Computational Physical Sciences (Ministry of Education), State Key Laboratory of Surface Physics, and Department of Physics, Fudan University, Shanghai 200433, People's Republic of China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, People's Republic of China
| | - L Bellaiche
- Physics Department and Institute for Nanoscience and Engineering, University of Arkansas, Fayetteville, Arkansas 72701, USA
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29
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Tao MJ, Zhang NN, Wen PY, Deng FG, Ai Q, Long GL. Coherent and incoherent theories for photosynthetic energy transfer. Sci Bull (Beijing) 2020; 65:318-328. [PMID: 36659097 DOI: 10.1016/j.scib.2019.12.009] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/21/2019] [Revised: 10/28/2019] [Accepted: 11/21/2019] [Indexed: 01/21/2023]
Abstract
There is a remarkable characteristic of photosynthesis in nature, that is, the energy transfer efficiency is close to 100%. Recently, due to the rapid progress made in the experimental techniques, quantum coherent effects have been experimentally demonstrated. Traditionally, the incoherent theories are capable of calculating the energy transfer efficiency, e.g., (generalized) Förster theory and modified Redfield theory (MRT). However, in order to describe the quantum coherent effects in photosynthesis, one has to exploit coherent theories, such as hierarchical equation of motion (HEOM), quantum path integral, coherent modified Redfield theory (CMRT), small-polaron quantum master equation, and general Bloch-Redfield theory in addition to the Redfield theory. Here, we summarize the main points of the above approaches, which might be beneficial to the quantum simulation of quantum dynamics of exciton energy transfer (EET) in natural photosynthesis, and shed light on the design of artificial light-harvesting devices.
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Affiliation(s)
- Ming-Jie Tao
- Department of Physics, Tsinghua University, Beijing 100084, China; Department of Physics, Applied Optics Beijing Area Major Laboratory, Beijing Normal University, Beijing 100875, China
| | - Na-Na Zhang
- Department of Physics, Applied Optics Beijing Area Major Laboratory, Beijing Normal University, Beijing 100875, China
| | - Peng-Yu Wen
- Department of Physics, Applied Optics Beijing Area Major Laboratory, Beijing Normal University, Beijing 100875, China
| | - Fu-Guo Deng
- Department of Physics, Applied Optics Beijing Area Major Laboratory, Beijing Normal University, Beijing 100875, China; NAAM-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
| | - Qing Ai
- Department of Physics, Applied Optics Beijing Area Major Laboratory, Beijing Normal University, Beijing 100875, China.
| | - Gui-Lu Long
- Department of Physics, Tsinghua University, Beijing 100084, China.
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30
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Amin ST, Mera B, Paunković N, Vieira VR. Information geometric analysis of long range topological superconductors. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019; 31:485402. [PMID: 31426047 DOI: 10.1088/1361-648x/ab3c70] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/05/2023]
Abstract
The Uhlmann connection is a mixed state generalisation of the Berry connection. The latter has a very important role in the study of topological phases at zero temperature. Closely related, the quantum fidelity is an information theoretical quantity which is a measure of distinguishability of quantum states. Moreover, it has been extensively used in the analysis of quantum phase transitions. In this work, we study topological phase transitions in 1D and 2D topological superconductors with long-range hopping and pairing amplitudes, using the fidelity and the quantity [Formula: see text] closely related to the Uhlmann connection. The drop in the fidelity and the departure of [Formula: see text] from zero signal the topological phase transitions in the models considered. The analysis of the ground state fidelity susceptibility and its associated critical exponents are also applied to the study of the aforementioned topological phase transitions.
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Affiliation(s)
- Syed Tahir Amin
- Instituto de Telecomunicações, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal. Departamento de Física, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal. CeFEMA, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal
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31
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Wei KX, Peng P, Shtanko O, Marvian I, Lloyd S, Ramanathan C, Cappellaro P. Emergent Prethermalization Signatures in Out-of-Time Ordered Correlations. PHYSICAL REVIEW LETTERS 2019; 123:090605. [PMID: 31524464 DOI: 10.1103/physrevlett.123.090605] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2018] [Indexed: 06/10/2023]
Abstract
How a many-body quantum system thermalizes-or fails to do so-under its own interaction is a fundamental yet elusive concept. Here we demonstrate nuclear magnetic resonance observation of the emergence of prethermalization by measuring out-of-time ordered correlations. We exploit Hamiltonian engineering techniques to tune the strength of spin-spin interactions and of a transverse magnetic field in a spin chain system, as well as to invert the Hamiltonian sign to reveal out-of-time ordered correlations. At large fields, we observe an emergent conserved quantity due to prethermalization, which can be revealed by an early saturation of correlations. Our experiment not only demonstrates a new protocol to measure out-of-time ordered correlations, but also provides new insights in the study of quantum thermodynamics.
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Affiliation(s)
- Ken Xuan Wei
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Pai Peng
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Oles Shtanko
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Iman Marvian
- Departments of Physics & Electrical and Computer Engineering, Duke University, Durham, North Carolina 27708, USA
| | - Seth Lloyd
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | | | - Paola Cappellaro
- Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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32
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Xu Z, Del Campo A. Probing the Full Distribution of Many-Body Observables By Single-Qubit Interferometry. PHYSICAL REVIEW LETTERS 2019; 122:160602. [PMID: 31075026 DOI: 10.1103/physrevlett.122.160602] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/07/2019] [Revised: 03/14/2019] [Indexed: 06/09/2023]
Abstract
We present an experimental scheme to measure the full distribution of many-body observables in spin systems, both in and out of equilibrium, using an auxiliary qubit as a probe. We focus on the determination of the magnetization and the kink number statistics at thermal equilibrium. The corresponding characteristic functions are related to the analytically continued partition function. Thus, both distributions can be directly extracted from experimental measurements of the coherence of a probe qubit that is coupled to an Ising-type bath, as reported in [X. Peng et al., Phys. Rev. Lett. 114, 010601 (2015)PRLTAO0031-900710.1103/PhysRevLett.114.010601] for the detection of Lee-Yang zeros.
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Affiliation(s)
- Zhenyu Xu
- School of Physical Science and Technology, Soochow University, Suzhou 215006, China
- Department of Physics, University of Massachusetts, Boston, Massachusetts 02125, USA
| | - Adolfo Del Campo
- Department of Physics, University of Massachusetts, Boston, Massachusetts 02125, USA
- Donostia International Physics Center, E-20018 San Sebastián, Spain
- IKERBASQUE, Basque Foundation for Science, E-48013 Bilbao, Spain
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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33
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Yang LP, Jacob Z. Quantum critical detector: amplifying weak signals using discontinuous quantum phase transitions. OPTICS EXPRESS 2019; 27:10482-10494. [PMID: 31052907 DOI: 10.1364/oe.27.010482] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/24/2019] [Accepted: 03/19/2019] [Indexed: 06/09/2023]
Abstract
We propose a quantum critical detector (QCD) to amplify weak input signals. Our detector exploits a first-order discontinuous quantum-phase-transition and exhibits giant sensitivity (χ ∝ N2) when biased at the critical point. We propose a model consisting of spins with long-range interactions coupled to a bosonic mode to describe the time-dynamics in the QCD. We numerically demonstrate dynamical features of the first order (discontinuous) quantum phase transition such as time-dependent quantum gain in a system with 80 interacting spins. We also show the linear scaling with the spin number N in both the quantum gain and the corresponding signal-to-quantum noise ratio during the time evolution of the device. Our work shows that engineering first order discontinuous quantum phase transitions can lead to a device application for metrology, weak signal amplification, and single photon detection.
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34
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Liu Y, Tian J, Betzholz R, Cai J. Pulsed Quantum-State Reconstruction of Dark Systems. PHYSICAL REVIEW LETTERS 2019; 122:110406. [PMID: 30951349 DOI: 10.1103/physrevlett.122.110406] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/29/2019] [Indexed: 06/09/2023]
Abstract
We propose a novel strategy to reconstruct the quantum state of dark systems, i.e., degrees of freedom that are not directly accessible for measurement or control. Our scheme relies on the quantum control of a two-level probe that exerts a state-dependent potential on the dark system. Using a sequence of control pulses applied to the probe makes it possible to tailor the information one can obtain and, for example, allows us to reconstruct the density operator of a dark spin as well as the Wigner characteristic function of a harmonic oscillator. Because of the symmetry of the applied pulse sequence, this scheme is robust against slow noise on the probe. The proof-of-principle experiments are readily feasible in solid-state spins and trapped ions.
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Affiliation(s)
- Yu Liu
- School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
- International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Jiazhao Tian
- School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
- International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Ralf Betzholz
- School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
- International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Jianming Cai
- School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
- International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China
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35
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Dynamical Quantum Phase Transition and Quasi Particle Excitation. Sci Rep 2019; 9:2871. [PMID: 30814602 PMCID: PMC6393518 DOI: 10.1038/s41598-019-39595-3] [Citation(s) in RCA: 41] [Impact Index Per Article: 8.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2018] [Accepted: 01/25/2019] [Indexed: 11/08/2022] Open
Abstract
Dynamical phase transitions (DPTs) are signaled by the non-analytical time evolution of the dynamical free energy after quenching some global parameters in quantum systems. The dynamical free energy is calculated from the overlap between the initial and the time evolved states (Loschmidt amplitude). In a recent study it was suggested that DPTs are related to the equilibrium phase transitions (EPTs) (Heyl, M. et al. Phys. Rev. Lett. 110, 135704 (2013)). We here study an exactly solvable model, the extended XY model, the Loschmidt amplitude of which provides a counterexample. We show analytically that the connection between the DPTs and the EPTs does not hold generally. Analysing also the general compass model as a second example, assists us to propound the physical condition under which the DPT occurs without crossing the equilibrium critical point, and also no DPT by crossing the equilibrium critical point.
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36
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Abstract
Quantum discord and entanglement are both criteria for distinguishing quantum correlations in a quantum system. We studied the effect of the transverse magnetic field on the quantum discord of the one-dimensional spin-1/2 XX model. This study focused on the pair of spins at different distances. We show that quantum discord is finite for all studied spin pairs in the Luttinger liquid phase. In addition, relying on our calculations, we show that the derivatives of quantum discord can be used to identify the border between entangled and separable regions in the Luttinger liquid phase.
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37
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Tonielli F, Fazio R, Diehl S, Marino J. Orthogonality Catastrophe in Dissipative Quantum Many-Body Systems. PHYSICAL REVIEW LETTERS 2019; 122:040604. [PMID: 30768302 DOI: 10.1103/physrevlett.122.040604] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/24/2018] [Revised: 01/09/2019] [Indexed: 06/09/2023]
Abstract
We present an analog of the phenomenon of orthogonality catastrophe in quantum many-body systems subject to a local dissipative impurity. We show that the fidelity F(t), giving a measure for distance of the time-evolved state from the initial one, displays a universal scaling form F(t)∝t^{θ}e^{-γt}, when the system supports long-range correlations, in a fashion reminiscent of traditional instances of orthogonality catastrophe in condensed matter. An exponential falloff at rate γ signals the onset of environmental decoherence, which is critically slowed down by the additional algebraic contribution to the fidelity. This picture is derived within a second-order cumulant expansion suited for Liouvillian dynamics, and substantiated for the one-dimensional transverse field quantum Ising model subject to a local dephasing jump operator, as well as for XY and XX quantum spin chains, and for the two-dimensional Bose gas deep in the superfluid phase with local particle heating. Our results hint that local sources of dissipation can be used to inspect real-time correlations and to induce a delay of decoherence in open quantum many-body systems.
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Affiliation(s)
- F Tonielli
- Institut für Theoretische Physik, Universität zu Köln, D-50937 Cologne, Germany
| | - R Fazio
- Abdus Salam ICTP, Strada Costiera 11, I-34151 Trieste, Italy and NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa, Italy
| | - S Diehl
- Institut für Theoretische Physik, Universität zu Köln, D-50937 Cologne, Germany
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106-4030, USA
| | - J Marino
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106-4030, USA
- Department of Physics, Harvard University, Cambridge Massachusetts 02138, USA and Department of Quantum Matter Physics, University of Geneva, 1211 Geneve, Switzerland
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38
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Cheraghi H, Mahdavifar S. Ineffectiveness of the Dzyaloshinskii-Moriya interaction in the dynamical quantum phase transition in the ITF model. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:42LT01. [PMID: 30222132 DOI: 10.1088/1361-648x/aae1c5] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Quantum phase transition occurs at a quantum critical value of a control parameter such as the magnetic field in the Ising model in a transverse magnetic field (ITF). Recently, it is shown that ramping across the quantum critical point generates non-analytic behaviors in the time evolution of a closed quantum system in the thermodynamic limit at zero temperature. The mentioned phenomenon is called the dynamical quantum phase transition (DQPT). Here, we consider the one-dimensional ITF model with added the Dzyaloshinskii-Moriya interaction (DMI). Using the fermionization technique, the Hamiltonian is exactly diagonalized. Although the DMI induces chiral phase in the ground state phase diagram of the model, the study of the rate function of the return probability has proven that the DMI does not affect the DQPT. We conclude accordingly that the ramping across the quantum critical point is not a necessary and sufficient condition for DQPT.
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Affiliation(s)
- Hadi Cheraghi
- Department of Physics, Semnan University, 35195-363, Semnan, Iran
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39
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Jose G, Malla R, Srinivasan V, Sharma A, Gangadharaiah S. Phase diagram for the Harper model of the honeycomb lattice. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:385603. [PMID: 30106380 DOI: 10.1088/1361-648x/aada3d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
The Harper equation arising out of a tight-binding model of electrons on a honeycomb lattice subject to a uniform magnetic field perpendicular to the plane is studied. Contrasting and complementary approaches involving von Neumann entropy, fidelity, fidelity susceptibility, and multifractal analysis are employed to characterize the phase diagram. Remarkably even in the absence of the quasi-periodic on-site potential term, the Hamiltonian allows for a metal-insulator transition. The phase diagram consists of three phases: two metallic phases and an insulating phase. A variant model where next nearest neighbor hopping is included, exhibits a mobility edge and does not allow for a simple single phase diagram characterizing all the eigenstates.
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Affiliation(s)
- Geo Jose
- Department of Physics, Indian Institute of Science Education and Research, Bhopal, India
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40
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Liu ZD, Lyyra H, Sun YN, Liu BH, Li CF, Guo GC, Maniscalco S, Piilo J. Experimental implementation of fully controlled dephasing dynamics and synthetic spectral densities. Nat Commun 2018; 9:3453. [PMID: 30150668 PMCID: PMC6110829 DOI: 10.1038/s41467-018-05817-x] [Citation(s) in RCA: 34] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2018] [Accepted: 07/26/2018] [Indexed: 11/17/2022] Open
Abstract
Engineering, controlling, and simulating quantum dynamics is a strenuous task. However, these techniques are crucial to develop quantum technologies, preserve quantum properties, and engineer decoherence. Earlier results have demonstrated reservoir engineering, construction of a quantum simulator for Markovian open systems, and controlled transition from Markovian to non-Markovian regime. Dephasing is an ubiquitous mechanism to degrade the performance of quantum computers. However, all-purpose quantum simulator for generic dephasing is still missing. Here, we demonstrate full experimental control of dephasing allowing us to implement arbitrary decoherence dynamics of a qubit. As examples, we use a photon to simulate the dynamics of a qubit coupled to an Ising chain in a transverse field and also demonstrate a simulation of nonpositive dynamical map. Our platform opens the possibility to simulate dephasing of any physical system and study fundamental questions on open quantum systems.
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Affiliation(s)
- Zhao-Di Liu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, People's Republic of China
| | - Henri Lyyra
- Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014, Turun yliopisto, Finland
| | - Yong-Nan Sun
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, People's Republic of China
| | - Bi-Heng Liu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, People's Republic of China
| | - Chuan-Feng Li
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China.
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, People's Republic of China.
| | - Guang-Can Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, People's Republic of China
| | - Sabrina Maniscalco
- Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014, Turun yliopisto, Finland
- Centre for Quantum Engineering, Department of Applied Physics, Aalto University, FI-00076, Aalto, Finland
| | - Jyrki Piilo
- Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014, Turun yliopisto, Finland.
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41
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Wang Q, Cao D, Quan HT. Effects of the Dzyaloshinsky-Moriya interaction on nonequilibrium thermodynamics in the XY chain in a transverse field. Phys Rev E 2018; 98:022107. [PMID: 30253493 DOI: 10.1103/physreve.98.022107] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2018] [Indexed: 06/08/2023]
Abstract
We examine the effects of the Dzyaloshinsky-Moriya (DM) interaction on the nonequilibrium thermodynamics in an anisotropic XY spin chain, which is driven out of equilibrium by a sudden quench of the control parameter of the Hamiltonian. By analytically evaluating the statistical properties of the work distribution and the irreversible entropy production, we investigate the influences of the DM interaction on the nonequilibrium thermodynamics of the system with different parameters at various temperatures. We find that depending on the anisotropy of the system and the temperature, the DM interaction may have different impacts on the nonequilibrium thermodynamics. Interestingly, the critical line induced by the DM interaction can be revealed via the properties of the nonequilibrium thermodynamics. In addition, our results suggest that the strength of the DM interaction can be detected experimentally by studying the nonequilibrium thermodynamics.
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Affiliation(s)
- Qian Wang
- Department of Physics, Zhejiang Normal University, Jinhua 321004, China
| | - Duo Cao
- Department of Physics, Shanghai Normal University, Shanghai 200234, China
| | - H T Quan
- School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
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42
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De Chiara G, Sanpera A. Genuine quantum correlations in quantum many-body systems: a review of recent progress. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2018; 81:074002. [PMID: 29671752 DOI: 10.1088/1361-6633/aabf61] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Quantum information theory has considerably helped in the understanding of quantum many-body systems. The role of quantum correlations and in particular, bipartite entanglement, has become crucial to characterise, classify and simulate quantum many body systems. Furthermore, the scaling of entanglement has inspired modifications to numerical techniques for the simulation of many-body systems leading to the, now established, area of tensor networks. However, the notions and methods brought by quantum information do not end with bipartite entanglement. There are other forms of correlations embedded in the ground, excited and thermal states of quantum many-body systems that also need to be explored and might be utilised as potential resources for quantum technologies. The aim of this work is to review the most recent developments regarding correlations in quantum many-body systems focussing on multipartite entanglement, quantum nonlocality, quantum discord, mutual information but also other non classical measures of correlations based on quantum coherence. Moreover, we also discuss applications of quantum metrology in quantum many-body systems.
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Affiliation(s)
- Gabriele De Chiara
- Centre for Theoretical Atomic, Molecular and Optical Physics, Queen's University Belfast, Belfast BT7 1NN, United Kingdom
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43
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Nag T, Rajak A. Entanglement entropy of a three-spin-interacting spin chain with a time-reversal-breaking impurity at one boundary. Phys Rev E 2018; 97:042108. [PMID: 29758713 DOI: 10.1103/physreve.97.042108] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2017] [Indexed: 06/08/2023]
Abstract
We investigate the effect of a time-reversal-breaking impurity term (of strength λ_{d}) on both the equilibrium and nonequilibrium critical properties of entanglement entropy (EE) in a three-spin-interacting transverse Ising model, which can be mapped to a p-wave superconducting chain with next-nearest-neighbor hopping and interaction. Importantly, we find that the logarithmic scaling of the EE with block size remains unaffected by the application of the impurity term, although, the coefficient (i.e., central charge) varies logarithmically with the impurity strength for a lower range of λ_{d} and eventually saturates with an exponential damping factor [∼exp(-λ_{d})] for the phase boundaries shared with the phase containing two Majorana edge modes. On the other hand, it receives a linear correction in term of λ_{d} for an another phase boundary. Finally, we focus to study the effect of the impurity in the time evolution of the EE for the critical quenching case where the impurity term is applied only to the final Hamiltonian. Interestingly, it has been shown that for all the phase boundaries, contrary to the equilibrium case, the saturation value of the EE increases logarithmically with the strength of impurity in a certain regime of λ_{d} and finally, for higher values of λ_{d}, it increases very slowly dictated by an exponential damping factor. The impurity-induced behavior of EE might bear some deep underlying connection to thermalization.
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Affiliation(s)
- Tanay Nag
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, Dresden 01187, Germany
| | - Atanu Rajak
- Department of Physics, Jack and Pearl Resnick Institute, Bar-Ilan University, Ramat-Gan 52900, Israel
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44
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Wang Q, Quan HT. Probing the excited-state quantum phase transition through statistics of Loschmidt echo and quantum work. Phys Rev E 2017; 96:032142. [PMID: 29347042 DOI: 10.1103/physreve.96.032142] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2017] [Indexed: 06/07/2023]
Abstract
By analyzing the probability distributions of the Loschmidt echo (LE) and quantum work, we examine the nonequilibrium effects of a quantum many-body system, which exhibits an excited-state quantum phase transition (ESQPT). We find that depending on the value of the controlling parameter the distribution of the LE displays different patterns. At the critical point of the ESQPT, both the averaged LE and the averaged work show a cusplike shape. Furthermore, by employing the finite-size scaling analysis of the averaged work, we obtain the critical exponent of the ESQPT. Finally, we show that at the critical point of ESQPT the eigenstate is a highly localized state, further highlighting the influence of the ESQPT on the properties of the many-body system.
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Affiliation(s)
- Qian Wang
- School of Physics, Peking University, Beijing 100871, China
- Department of Physics, Shanghai Normal University, Shanghai 200234, China
| | - H T Quan
- School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
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45
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Ma YH, Su SH, Sun CP. Quantum thermodynamic cycle with quantum phase transition. Phys Rev E 2017; 96:022143. [PMID: 28950560 DOI: 10.1103/physreve.96.022143] [Citation(s) in RCA: 38] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2017] [Indexed: 11/07/2022]
Abstract
With the Lipkin-Meshkov-Glick (LMG) model as an illustration, we construct a thermodynamic cycle composed of two isothermal processes and two isomagnetic field processes, and we study the thermodynamic performance of this cycle accompanied by the quantum phase transition (QPT). We find that for a finite particle system working below the critical temperature, the efficiency of the cycle is capable of approaching the Carnot limit when the external magnetic field λ_{1} corresponding to one of the isomagnetic processes reaches the cross point of the ground states' energy level, which can become the critical point of the QPT in the large-N limit. Our analysis proves that the system's energy level crossings at low-temperature limits can lead to a significant improvement in the efficiency of the quantum heat engine. In the case of the thermodynamics limit (N→∞), the analytical partition function is obtained to study the efficiency of the cycle at high- and low-temperature limits. At low temperatures, when the magnetic fields of the isothermal processes are located on both sides of the critical point of the QPT, the cycle reaches maximum efficiency, and the Carnot efficiency can be achieved. This observation demonstrates that the QPT of the LMG model below critical temperature is beneficial to the thermodynamic cycle's operation.
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Affiliation(s)
- Yu-Han Ma
- Beijing Computational Science Research Center, Beijing 100193, China.,Graduate School of Chinese Academy of Engineering Physics, Beijing 100084, China
| | - Shan-He Su
- Beijing Computational Science Research Center, Beijing 100193, China
| | - Chang-Pu Sun
- Beijing Computational Science Research Center, Beijing 100193, China.,Graduate School of Chinese Academy of Engineering Physics, Beijing 100084, China
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46
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Zhang G, Li C, Song Z. Majorana charges, winding numbers and Chern numbers in quantum Ising models. Sci Rep 2017; 7:8176. [PMID: 28811635 PMCID: PMC5558019 DOI: 10.1038/s41598-017-08323-0] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/13/2016] [Accepted: 07/07/2017] [Indexed: 11/18/2022] Open
Abstract
Mapping a many-body state on a loop in parameter space is a simple way to characterize a quantum state. The connections of such a geometrical representation to the concepts of Chern number and Majorana zero mode are investigated based on a generalized quantum spin system with short and long-range interactions. We show that the topological invariants, the Chern numbers of corresponding Bloch band, is equivalent to the winding number in the auxiliary plane, which can be utilized to characterize the phase diagram. We introduce the concept of Majorana charge, the magnitude of which is defined by the distribution of Majorana fermion probability in zero-mode states, and the sign is defined by the type of Majorana fermion. By direct calculations of the Majorana modes we analytically and numerically verify that the Majorana charge is equal to Chern numbers and winding numbers.
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Affiliation(s)
- G Zhang
- College of Physics and Materials Science, Tianjin Normal University, Tianjin, 300387, China.,School of Physics, Nankai University, Tianjin, 300071, China
| | - C Li
- School of Physics, Nankai University, Tianjin, 300071, China
| | - Z Song
- School of Physics, Nankai University, Tianjin, 300071, China.
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47
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Hu T, Xue K, Li X, Zhang Y, Ren H. Excited-state fidelity as a signal for the many-body localization transition in a disordered Ising chain. Sci Rep 2017; 7:577. [PMID: 28373700 PMCID: PMC5475297 DOI: 10.1038/s41598-017-00660-4] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2016] [Accepted: 03/07/2017] [Indexed: 11/30/2022] Open
Abstract
In this work, we use exact matrix diagonalization to explore the many-body localization (MBL) transitions in quantum Ising chains with disordered nearest-neighbour couplings, disordered next-nearest-neighbour couplings and disordered external fields. It is demonstrated that the fidelity can be used to characterize the interaction-driven MBL transition in this closed spin system in a manner that is consistent with previous analytical and numerical results. We compute the fidelity for high-energy many-body eigenstates, namely, the excited-state fidelity. It is demonstrated that disordered nearest-neighbour couplings, disordered next-nearest-neighbour couplings and disordered external fields each have different effects on the MBL transition. Furthermore, we investigate the MBL transition of a quantum Ising chain with both disordered nearest-neighbour couplings and disordered next-nearest-neighbour couplings to see how these two types of disordered couplings drive the occurrence of the MBL transition.
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Affiliation(s)
- Taotao Hu
- School of Physics, Northeast Normal University, Changchun, 130024, People's Republic of China.
| | - Kang Xue
- School of Physics, Northeast Normal University, Changchun, 130024, People's Republic of China
| | - Xiaodan Li
- College of Science, University of Shanghai for Science and Technology, Shanghai, 200093, People's Republic of China
| | - Yan Zhang
- School of Physics, Northeast Normal University, Changchun, 130024, People's Republic of China
| | - Hang Ren
- Key Laboratory of Airborne Optical Imaging and Measurement, Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun, 130033, People's Republic of China
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48
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Jafari R, Johannesson H. Loschmidt Echo Revivals: Critical and Noncritical. PHYSICAL REVIEW LETTERS 2017; 118:015701. [PMID: 28106441 DOI: 10.1103/physrevlett.118.015701] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/24/2016] [Indexed: 06/06/2023]
Abstract
A quantum phase transition is generally thought to imprint distinctive characteristics on the nonequilibrium dynamics of a closed quantum system. Specifically, the Loschmidt echo after a sudden quench to a quantum critical point-measuring the time dependence of the overlap between initial and time-evolved states-is expected to exhibit an accelerated relaxation followed by periodic revivals. We here introduce a new exactly solvable model, the extended Su-Schrieffer-Heeger model, the Loschmidt echo of which provides a counterexample. A parallell analysis of the quench dynamics of the three-site spin-interacting XY model allows us to pinpoint the conditions under which a periodic Loschmidt revival actually appears.
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Affiliation(s)
- R Jafari
- Beijing Computational Science Research Center, Beijing 100094, China
- Department of Physics, University of Gothenburg, SE 412 96 Gothenburg, Sweden
- Department of Physics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45137-66731, Iran
| | - Henrik Johannesson
- Beijing Computational Science Research Center, Beijing 100094, China
- Department of Physics, University of Gothenburg, SE 412 96 Gothenburg, Sweden
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Yang W, Ma WL, Liu RB. Quantum many-body theory for electron spin decoherence in nanoscale nuclear spin baths. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2017; 80:016001. [PMID: 27811398 DOI: 10.1088/0034-4885/80/1/016001] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Decoherence of electron spins in nanoscale systems is important to quantum technologies such as quantum information processing and magnetometry. It is also an ideal model problem for studying the crossover between quantum and classical phenomena. At low temperatures or in light-element materials where the spin-orbit coupling is weak, the phonon scattering in nanostructures is less important and the fluctuations of nuclear spins become the dominant decoherence mechanism for electron spins. Since the 1950s, semi-classical noise theories have been developed for understanding electron spin decoherence. In spin-based solid-state quantum technologies, the relevant systems are in the nanometer scale and nuclear spin baths are quantum objects which require a quantum description. Recently, quantum pictures have been established to understand the decoherence and quantum many-body theories have been developed to quantitatively describe this phenomenon. Anomalous quantum effects have been predicted and some have been experimentally confirmed. A systematically truncated cluster-correlation expansion theory has been developed to account for the many-body correlations in nanoscale nuclear spin baths that are built up during electron spin decoherence. The theory has successfully predicted and explained a number of experimental results in a wide range of physical systems. In this review, we will cover this recent progress. The limitations of the present quantum many-body theories and possible directions for future development will also be discussed.
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Affiliation(s)
- Wen Yang
- Beijing Computational Science Research Center, Beijing 100193, People's Republic of China
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Hu T, Xue K, Li X, Zhang Y, Ren H. Fidelity of the diagonal ensemble signals the many-body localization transition. Phys Rev E 2016; 94:052119. [PMID: 27967130 DOI: 10.1103/physreve.94.052119] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/13/2016] [Indexed: 11/07/2022]
Abstract
In this work, we use exact matrix diagonalization to explore the many-body localization (MBL) transition in a random-field Heisenberg chain. We demonstrate that the fidelity and fidelity susceptibility can be utilized to characterize the interaction-driven many-body localization transition in this closed spin system which is in agreement with previous analytical and numerical results [S. Garnerone, N. T. Jacobson, S. Haas, and P. Zanardi, Phys. Rev. Lett. 102, 057205 (2009)PRLTAO0031-900710.1103/PhysRevLett.102.057205; P. Zanardi and N. Paunkovic, Phys. Rev. E 74, 031123 (2006)PLEEE81539-375510.1103/PhysRevE.74.031123]. In particular, instead of ground-state fidelity, we test the fidelity between two diagonal ensembles related by a small parameter perturbation δh, it is special that here the parameter perturbation δh_{i} for each site are random variables like h_{i}. It shows that fidelity of the diagonal ensemble develop a pronounced drop at the transition. We utilize fidelity to estimate the critical disorder strength h_{c} for different system size, we get h_{c}∈ [2.5,3.9] and get a power-law decay with an exponent of roughly -1.49(2) for system size N, and can extrapolate h_{c}^{inf} of the infinite system is about 2.07 which all agree with a recent work by Huse and Pal, in which the MBL transition in the same model was predicted to be hc [2,4]. We also estimate the scaling of maximum of averaged fidelity susceptibility as a function of system size N, it shows a power law increase with an exponent of about 5.05(1).
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Affiliation(s)
- Taotao Hu
- School of Physics, Northeast Normal University, Changchun 130024, People's Republic of China
| | - Kang Xue
- School of Physics, Northeast Normal University, Changchun 130024, People's Republic of China
| | - Xiaodan Li
- College of Science, University of Shanghai for Science and Technology, Shanghai 200093, People's Republic of China
| | - Yan Zhang
- School of Physics, Northeast Normal University, Changchun 130024, People's Republic of China
| | - Hang Ren
- Key Laboratory of Airborne Optical Imaging and Measurement, Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, Peoples Republic of China
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