1
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Wang Z, Liu Y, Wang B. Bond-Orbital-Resolved Piezoelectricity in Sp 2-Hybridized Monolayer Semiconductors. MATERIALS (BASEL, SWITZERLAND) 2022; 15:7788. [PMID: 36363380 PMCID: PMC9653688 DOI: 10.3390/ma15217788] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/03/2022] [Revised: 10/31/2022] [Accepted: 11/01/2022] [Indexed: 06/16/2023]
Abstract
Sp2-hybridized monolayer semiconductors (e.g., planar group III-V and IV-IV binary compounds) with inversion symmetry breaking (ISB) display piezoelectricity governed by their σ- and π-bond electrons. Here, we studied their bond-orbital-resolved electronic piezoelectricity (i.e., the σ- and π-piezoelectricity). We formulated a tight-binding piezoelectric model to reveal the different variations of σ- and π-piezoelectricity with the ISB strength (Δ). As Δ varied from positive to negative, the former decreased continuously, but the latter increased piecewise and jumped at Δ=0 due to the criticality of the π-electrons' ground-state geometry near this quantum phase-transition point. This led to a piezoelectricity predominated by the π-electrons for a small |Δ|. By constructing an analytical model, we clarified the microscopic mechanisms underlying the anomalous π-piezoelectricity and its subtle relations with the valley Hall effect. The validation of our models was justified by applying them to the typical sp2 monolayers including hexagonal silicon carbide, Boron-X (X = N, P, As, Ab), and a BN-doped graphene superlattice.
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Affiliation(s)
- Zongtan Wang
- School of Aeronautics and Astronautics, Sun Yat-sen University, Shenzhen 518000, China
| | - Yulan Liu
- School of Aeronautics and Astronautics, Sun Yat-sen University, Shenzhen 518000, China
| | - Biao Wang
- Sino-Franch Institute of Nuclear Engineering and Technology, Sun Yat-sen University, Zhuhai 519082, China
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2
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Austrich-Olivares JA, Vergara JD. The Quantum Geometric Tensor in a Parameter-Dependent Curved Space. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1236. [PMID: 36141122 PMCID: PMC9497705 DOI: 10.3390/e24091236] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/28/2022] [Revised: 08/18/2022] [Accepted: 08/27/2022] [Indexed: 06/16/2023]
Abstract
We introduce a quantum geometric tensor in a curved space with a parameter-dependent metric, which contains the quantum metric tensor as the symmetric part and the Berry curvature corresponding to the antisymmetric part. This parameter-dependent metric modifies the usual inner product, which induces modifications in the quantum metric tensor and Berry curvature by adding terms proportional to the derivatives with respect to the parameters of the determinant of the metric. The quantum metric tensor is obtained in two ways: By using the definition of the infinitesimal distance between two states in the parameter-dependent curved space and via the fidelity susceptibility approach. The usual Berry connection acquires an additional term with which the curved inner product converts the Berry connection into an object that transforms as a connection and density of weight one. Finally, we provide three examples in one dimension with a nontrivial metric: an anharmonic oscillator, a Morse-like potential, and a generalized anharmonic oscillator; and one in two dimensions: the coupled anharmonic oscillator in a curved space.
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3
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Jaiswal N, Gautam M, Sarkar T. Complexity and information geometry in the transverse XY model. Phys Rev E 2021; 104:024127. [PMID: 34525655 DOI: 10.1103/physreve.104.024127] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/11/2020] [Accepted: 08/05/2021] [Indexed: 11/07/2022]
Abstract
We study Nielsen complexity and Fubini-Study complexity for the transverse XY spin chain and establish their nonanalyticity at the critical lines. We obtain the scaling behavior of both complexities near quantum phase transitions in the thermodynamic limit, as a function of the system parameters. The scaling of the Nielsen complexity with the system size is also established, close to criticality. We also obtain analytic expressions for the Fubini-Study complexity in some special cases for this model, while a numerical analysis in more generic situations is carried out. Our study clearly demonstrates the differences in the two notions of complexity in the transverse XY model.
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Affiliation(s)
- Nitesh Jaiswal
- Department of Physics, Indian Institute of Technology, Kanpur-208016, India
| | - Mamta Gautam
- Department of Physics, Indian Institute of Technology, Kanpur-208016, India
| | - Tapobrata Sarkar
- Department of Physics, Indian Institute of Technology, Kanpur-208016, India
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4
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Liu YG, Xu L, Li Z. Quantum phase transition in a non-Hermitian XYspin chain with global complex transverse field. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:295401. [PMID: 33984851 DOI: 10.1088/1361-648x/ac00dd] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2021] [Accepted: 05/13/2021] [Indexed: 06/12/2023]
Abstract
In this work, we investigate the quantum phase transition in a non-HermitianXYspin chain. The phase diagram shows that the critical points of Ising phase transition expand into a critical transition zone after introducing a non-Hermitian effect. By analyzing the non-Hermitian gap and long-range correlation function, one can distinguish different phases by means of different gap features and decay properties of correlation function, a tricky problem in traditionalXYmodel. Furthermore, the results reveal the relationship among different regions of the phase diagram, non-Hermitian energy gap and long-range correlation function.
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Affiliation(s)
- Yu-Guo Liu
- School of Physics, Nanjing University, Nanjing 210093, People's Republic of China
- National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, People's Republic of China
| | - Lu Xu
- School of Physics, Nanjing University, Nanjing 210093, People's Republic of China
- National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, People's Republic of China
| | - Zhi Li
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, SPTE, South China Normal University, Guangzhou 510006, People's Republic of China
- GPETR Center for Quantum Precision Measurement, South China Normal University, Guangzhou 510006, People's Republic of China
- Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, People's Republic of China
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5
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Abstract
We study the scaling behavior of the Berry phase in the Yang-Lee edge singularity (YLES) of the non-Hermitian quantum system. A representative model, the one-dimensional quantum Ising model in an imaginary longitudinal field, is selected. For this model, the dissipative phase transition (DPT), accompanying a parity-time (PT) symmetry-breaking phase transition, occurs when the imaginary field changes through the YLES. We find that the real and imaginary parts of the complex Berry phase show anomalies around the critical points of YLES. In the overlapping critical regions constituted by the (0 + 1)D YLES and (1 + 1)D ferromagnetic-paramagnetic phase transition (FPPT), we find that the real and imaginary parts of the Berry phase can be described by both the (0 + 1)D YLES and (1 + 1)D FPPT scaling theory. Our results demonstrate that the complex Berry phase can be used as a universal order parameter for the description of the critical behavior and the phase transition in the non-Hermitian systems.
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6
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Lu B, Liu XF, Gao YP, Cao C, Wang TJ, Wang C. Berry phase in an anti-PT symmetric metal-semiconductor complex system. OPTICS EXPRESS 2019; 27:22237-22245. [PMID: 31510520 DOI: 10.1364/oe.27.022237] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/08/2019] [Accepted: 07/03/2019] [Indexed: 06/10/2023]
Abstract
Berry phase can be used to generate quantum state which is robust to environmental noises in quantum information processing. Recently, the relationship between Berry phase and quantum phase transition attracts great attention in the research about topological states of matter. Here, we investigate the behavior of Berry phase in an anti parity-time symmetric system consisting of a metal nanoparticle and semiconductor quantum dot. The change of Berry phase undergoes a sudden death around exceptional point, i.e., Berry phase keeps unchanged in symmetry unbroken region, while it can be well adjusted through changing the strength and frequency of input light in symmetry broken region. The result demonstrated in this paper may be of significant importance in quantum computation and topological physics.
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7
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Yang XM, Zhang G, Song Z. Phase transition in phase transition lines of quantum XY model. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019; 31:245401. [PMID: 30861505 DOI: 10.1088/1361-648x/ab0f04] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Phase transitions in quantum systems, including symmetry breaking and topological types, always associate with gap closing and opening. We analyze the topological features of the quantum phase boundary of the XY model in a transverse magnetic field. Based on the results from graphs in the auxiliary space, we find that gapless ground states at boundary have different topological characters. On the other hand, in the framework of Majorana representation, the Majorana lattice is shown to be two coupled SSH chains. The analysis of the quantum fidelity for the Majorana eigen vector, which is shown to be identical to the square of that for ground states of the XY model, indicates the signature of the gapless phase transition (GPT). Furthermore analytical and numerical results for second-order derivative of groundstate energy density show that such a GPT obeys scaling behavior.
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Affiliation(s)
- X M Yang
- School of Physics, Nankai University, Tianjin 300071, People's Republic of China
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8
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Analysis of the geometric phase for a nanowire-bridged superconducting Fabry-Perot resonator. Sci Rep 2019; 9:8428. [PMID: 31182767 PMCID: PMC6557848 DOI: 10.1038/s41598-019-44754-7] [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: 11/06/2018] [Accepted: 05/15/2019] [Indexed: 11/09/2022] Open
Abstract
The geometric phases of a nanowire-bridged superconducting Fabry-Perot resonator subjected to a microwave transmission have been investigated through its modelling into a RLC-circuit. Because the Hamiltonian of the system is a somewhat complicated form, special mathematical techniques, such as the invariant operator method and the unitary transformation approach, have been adopted in order to treat the system; These methods are very useful for managing complicated time-dependent Hamiltonian systems. We have rigorously evaluated the analytical geometric phases in both the Fock and coherent states. Typically, the geometric phases oscillate and the amplitude of such oscillations tend to grow over time. The influence of parameters of the system on the geometric phases has been analyzed in detail through the relevant illustrations. From our research, the concept of geometric phases and associated quantum mechanical characters of the system has been clarified. Our investigation for the geometric phases is useful for understanding topological features of the system, that take place through the evolution of the wave functions.
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9
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Tan X, Zhang DW, Yang Z, Chu J, Zhu YQ, Li D, Yang X, Song S, Han Z, Li Z, Dong Y, Yu HF, Yan H, Zhu SL, Yu Y. Experimental Measurement of the Quantum Metric Tensor and Related Topological Phase Transition with a Superconducting Qubit. PHYSICAL REVIEW LETTERS 2019; 122:210401. [PMID: 31283314 DOI: 10.1103/physrevlett.122.210401] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/04/2019] [Indexed: 06/09/2023]
Abstract
A Berry curvature is an imaginary component of the quantum geometric tensor (QGT) and is well studied in many branches of modern physics; however, the quantum metric as a real component of the QGT is less explored. Here, by using tunable superconducting circuits, we experimentally demonstrate two methods to directly measure the quantum metric tensor for characterizing the geometry and topology of underlying quantum states in parameter space. The first method is to probe the transition probability after a sudden quench, and the second one is to detect the excitation rate under weak periodic driving. Furthermore, based on quantum metric and Berry-curvature measurements, we explore a topological phase transition in a simulated time-reversal-symmetric system. The work opens up a unique approach to explore the topology of quantum states with the QGT.
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Affiliation(s)
- Xinsheng Tan
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Dan-Wei Zhang
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, GPETR Center for Quantum Precision Measurement and SPTE, South China Normal University, Guangzhou 510006, China
| | - Zhen Yang
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Ji Chu
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Yan-Qing Zhu
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Danyu Li
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Xiaopei Yang
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Shuqing Song
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Zhikun Han
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Zhiyuan Li
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Yuqian Dong
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Hai-Feng Yu
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Hui Yan
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, GPETR Center for Quantum Precision Measurement and SPTE, South China Normal University, Guangzhou 510006, China
| | - Shi-Liang Zhu
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, GPETR Center for Quantum Precision Measurement and SPTE, South China Normal University, Guangzhou 510006, China
| | - Yang Yu
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
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10
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Gonzalez D, Gutiérrez-Ruiz D, Vergara JD. Classical analog of the quantum metric tensor. Phys Rev E 2019; 99:032144. [PMID: 30999496 DOI: 10.1103/physreve.99.032144] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2018] [Indexed: 11/07/2022]
Abstract
We present a classical analog of the quantum metric tensor, which is defined for classical integrable systems that undergo an adiabatic evolution governed by slowly varying parameters. This classical metric measures the distance, on the parameter space, between two infinitesimally different points in phase space, whereas the quantum metric tensor measures the distance between two infinitesimally different quantum states. We discuss the properties of this metric and calculate its components, exactly in the cases of the generalized harmonic oscillator, the generalized harmonic oscillator with a linear term, and perturbatively for the quartic anharmonic oscillator. Finally, we propose alternative expressions for the quantum metric tensor and Berry's connection in terms of quantum operators.
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Affiliation(s)
- Diego Gonzalez
- Departamento de Física de Altas Energías, Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, Ciudad de México 04510, México
| | - Daniel Gutiérrez-Ruiz
- Departamento de Física de Altas Energías, Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, Ciudad de México 04510, México
| | - J David Vergara
- Departamento de Física de Altas Energías, Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, Ciudad de México 04510, México
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11
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Requist R, Gross EKU. Accurate Formula for the Macroscopic Polarization of Strongly Correlated Materials. J Phys Chem Lett 2018; 9:7045-7051. [PMID: 30501191 DOI: 10.1021/acs.jpclett.8b03028] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
The many-body Berry phase formula for macroscopic polarization is approximated by a sum of natural orbital geometric phases with fractional occupation numbers accounting for the dominant correlation effects. This formula accurately reproduces the exact polarization in the Rice-Mele-Hubbard model across the band insulator-Mott insulator transition. A similar formula based on a reduced Berry curvature accurately predicts the interaction-induced quenching of Thouless topological charge pumping.
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Affiliation(s)
- Ryan Requist
- Max Planck Institute of Microstructure Physics , Weinberg 2 , 06114 Halle , Germany
| | - E K U Gross
- Max Planck Institute of Microstructure Physics , Weinberg 2 , 06114 Halle , Germany
- Fritz Haber Center for Molecular Dynamics, Institute of Chemistry , The Hebrew University of Jerusalem , Jerusalem 91904 , Israel
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12
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Luo Q, Zhao J, Wang X. Fidelity susceptibility of the anisotropic XY model: The exact solution. Phys Rev E 2018; 98:022106. [PMID: 30253491 DOI: 10.1103/physreve.98.022106] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2018] [Indexed: 06/08/2023]
Abstract
We derive several closed-form expressions for the fidelity susceptibility (FS) of the anisotropic XY model in the transverse field. The basic idea lies in a partial fraction expansion of the expression so that all the terms are related to a simple fraction or its derivative. The critical points of the model are reiterated by the FS, demonstrating its validity for characterizing the phase transitions. Moreover, the critical exponents ν associated with the correlation length in both critical regions are successfully extracted by the standard finite-size scaling analysis.
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Affiliation(s)
- Qiang Luo
- Department of Physics, Renmin University of China, Beijing 100872, China
| | - Jize Zhao
- Center for Interdisciplinary Studies, Lanzhou University, Lanzhou 730000, China
| | - Xiaoqun Wang
- Key Laboratory of Artificial Structures and Quantum Control, Ministry of Education, School of Physics and Astronomy, Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai 200240, China
- Collaborative Innovation Center for Advanced Microstructures, Nanjing 210093, China
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13
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Carollo A, Spagnolo B, Valenti D. Uhlmann curvature in dissipative phase transitions. Sci Rep 2018; 8:9852. [PMID: 29959332 PMCID: PMC6026214 DOI: 10.1038/s41598-018-27362-9] [Citation(s) in RCA: 92] [Impact Index Per Article: 15.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2018] [Accepted: 05/10/2018] [Indexed: 11/09/2022] Open
Abstract
A novel approach based on the Uhlmann curvature is introduced for the investigation of non-equilibrium steady-state quantum phase transitions (NESS-QPTs). Equilibrium phase transitions fall invariably into two markedly non-overlapping categories: classical phase transitions and quantum phase transitions. NESS-QPTs offer a unique arena where such a distinction fades off. We propose a method to reveal and quantitatively assess the quantum character of such critical phenomena. We apply this tool to a paradigmatic class of lattice fermion systems with local reservoirs, characterised by Gaussian non-equilibrium steady states. The relations between the behaviour of the Uhlmann curvature, the divergence of the correlation length, the character of the criticality and the dissipative gap are demonstrated. We argue that this tool can shade light upon the nature of non equilibrium steady state criticality in particular with regard to the role played by quantum vs classical fluctuations.
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Affiliation(s)
- Angelo Carollo
- Department of Physics and Chemistry, Group of Interdisciplinary Theoretical Physics, University of Palermo, Viale delle Scienze, Ed. 18, I-90128, Palermo, Italy. .,Radiophysics Department, Lobachevsky State University of Nizhni Novgorod, 23 Gagarin Avenue, Nizhni, Novgorod, 603950, Russia.
| | - Bernardo Spagnolo
- Department of Physics and Chemistry, Group of Interdisciplinary Theoretical Physics, University of Palermo, Viale delle Scienze, Ed. 18, I-90128, Palermo, Italy.,Radiophysics Department, Lobachevsky State University of Nizhni Novgorod, 23 Gagarin Avenue, Nizhni, Novgorod, 603950, Russia.,Istituto Nazionale di Fisica Nucleare, Sezione di Catania, Via S. Sofia 64, I-90123, Catania, Italy
| | - Davide Valenti
- Department of Physics and Chemistry, Group of Interdisciplinary Theoretical Physics, University of Palermo, Viale delle Scienze, Ed. 18, I-90128, Palermo, Italy.,Istituto di Biomedicina ed Immunologia Molecolare (IBIM) "Alberto Monroy", CNR, Via Ugo La Malfa 153, I-90146, Palermo, Italy
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14
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Symmetric Logarithmic Derivative of Fermionic Gaussian States. ENTROPY 2018; 20:e20070485. [PMID: 33265575 PMCID: PMC7513002 DOI: 10.3390/e20070485] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Received: 05/21/2018] [Revised: 06/16/2018] [Accepted: 06/16/2018] [Indexed: 01/24/2023]
Abstract
In this article, we derive a closed form expression for the symmetric logarithmic derivative of Fermionic Gaussian states. This provides a direct way of computing the quantum Fisher Information for Fermionic Gaussian states. Applications range from quantum Metrology with thermal states to non-equilibrium steady states with Fermionic many-body systems.
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15
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Nie W, Mei F, Amico L, Kwek LC. Scaling of geometric phase versus band structure in cluster-Ising models. Phys Rev E 2017; 96:020106. [PMID: 28950507 DOI: 10.1103/physreve.96.020106] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2017] [Indexed: 11/07/2022]
Abstract
We study the phase diagram of a class of models in which a generalized cluster interaction can be quenched by an Ising exchange interaction and external magnetic field. The various phases are studied through winding numbers. They may be ordinary phases with local order parameters or exotic ones, known as symmetry protected topologically ordered phases. Quantum phase transitions with dynamical critical exponents z=1 or z=2 are found. In particular, the criticality is analyzed through finite-size scaling of the geometric phase accumulated when the spins of the lattice perform an adiabatic precession. With this study, we quantify the scaling behavior of the geometric phase in relation to the topology and low-energy properties of the band structure of the system.
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Affiliation(s)
- Wei Nie
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
| | - Feng Mei
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan, Shanxi 030006, China.,Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Luigi Amico
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore.,Dipartimento di Fisica e Astronomia, Universitá Catania, Via S. Sofia 64, I-95123 Catania, Italy.,CNR-IMM UOS Università (MATIS), Consiglio Nazionale delle Ricerche & INFN, Sezione di Catania, Via Santa Sofia 64, I-95123 Catania, Italy.,LANEF "Chaire d'excellence", Université Grenoble-Alpes & CNRS, F-38000 Grenoble, France.,MajuLab, CNRS-UNS-NUS-NTU International Joint Research Unit, UMI 3654, Singapore
| | - Leong Chuan Kwek
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore.,MajuLab, CNRS-UNS-NUS-NTU International Joint Research Unit, UMI 3654, Singapore.,Institute of Advanced Studies, Nanyang Technological University, 60 Nanyang View, Singapore 639673, Singapore.,National Institute of Education, Nanyang Technological University, 1 Nanyang Walk, Singapore 637616, Singapore
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16
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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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17
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Abstract
We study the connections between local quantum coherence (LQC) based on Wigner-Yanase skew information and quantum phase transitions (QPTs). When applied on the one-dimensional Hubbard, XY spin chain with three-spin interaction, and Su-Schrieffer-Heeger models, the LQC and its derivatives are used successfully to detect different types of QPTs in these spin and fermionic systems. Furthermore, the LQC is effective as the quantum discord (QD) in detecting QPTs at finite temperatures, where the entanglement has lost its effectiveness. We also demonstrate that the LQC can exhibit different behaviors in many forms compared with the QD.
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18
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Wei YB, Zou J, Wang ZM, Shao B. Quantum speed limit and a signal of quantum criticality. Sci Rep 2016; 6:19308. [PMID: 26782296 PMCID: PMC4725993 DOI: 10.1038/srep19308] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2015] [Accepted: 12/09/2015] [Indexed: 11/12/2022] Open
Abstract
We study the quantum speed limit time (QSLT) of a coupled system consisting of a central spin and its surrounding environment, and the environment is described by a general XY spin-chain model. For initial pure state, we find that the local anomalous enhancement of the QSLT occurs near the critical point. In addition, we investigate the QSLT for arbitrary time-evolution state in the whole dynamics process and find that the QSLT will decay monotonously and rapidly at a large size of environment near the quantum critical point. These anomalous behaviors in the critical vicinity of XY spin-chain environment can be used to indicate the quantum phase transition point. Especially for the XX spin-chain environment, we find that the QSLT displays a sudden transition from discontinuous segmented values to a steady value at the critical point. In this case, the non-Makovianity and the Loschmidt echo are incapable of signaling the critical value of the transverse field, while the QSLT can still witness the quantum phase transition. So, the QSLT provides a further insight and sharper identification of quantum criticality.
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Affiliation(s)
- Yong-Bo Wei
- School of Physics, Beijing Institute of Technology, Beijing 100081, China
| | - Jian Zou
- School of Physics, Beijing Institute of Technology, Beijing 100081, China
| | - Zhao-Ming Wang
- Department of Physics, Ocean University of China, Qingdao 266100, China
| | - Bin Shao
- School of Physics, Beijing Institute of Technology, Beijing 100081, China
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19
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Castaños O, Calixto M, Pérez-Bernal F, Romera E. Identifying the order of a quantum phase transition by means of Wehrl entropy in phase space. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:052106. [PMID: 26651646 DOI: 10.1103/physreve.92.052106] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/25/2015] [Indexed: 06/05/2023]
Abstract
We propose a method to identify the order of a quantum phase transition by using area measures of the ground state in phase space. We illustrate our proposal by analyzing the well known example of the quantum cusp and four different paradigmatic boson models: Dicke, Lipkin-Meshkov-Glick, interacting boson model, and vibron model.
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Affiliation(s)
- Octavio Castaños
- Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, 04510 Distrito Federal, Mexico
| | - Manuel Calixto
- Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, Fuentenueva s/n, 18071 Granada, Spain
| | - Francisco Pérez-Bernal
- Departamento de Física Aplicada, Facultad de Ciencias Experimentales, Universidad de Huelva, Campus del Carmen, Avenida de las Fuerzas Armadas s/n, 21071 Huelva, Spain
| | - Elvira Romera
- Departamento de Física Atómica, Molecular y Nuclear and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Fuentenueva s/n, 18071 Granada, Spain
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20
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Ma YQ. Quantum distance and the Euler number index of the Bloch band in a one-dimensional spin model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:042133. [PMID: 25375464 DOI: 10.1103/physreve.90.042133] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/04/2014] [Indexed: 06/04/2023]
Abstract
We study the Riemannian metric and the Euler characteristic number of the Bloch band in a one-dimensional spin model with multisite spins exchange interactions. The Euler number of the Bloch band originates from the Gauss-Bonnet theorem on the topological characterization of the closed Bloch states manifold in the first Brillouin zone. We study this approach analytically in a transverse field XY spin chain with three-site spin coupled interactions. We define a class of cyclic quantum distance on the Bloch band and on the ground state, respectively, as a local characterization for quantum phase transitions. Specifically, we give a general formula for the Euler number by means of the Berry curvature in the case of two-band models, which reveals its essential relation to the first Chern number of the band insulators. Finally, we show that the ferromagnetic-paramagnetic phase transition in zero temperature can be distinguished by the Euler number of the Bloch band.
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Affiliation(s)
- Yu-Quan Ma
- School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, China
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21
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Mascarenhas E, Bragança H, Dorner R, França Santos M, Vedral V, Modi K, Goold J. Work and quantum phase transitions: quantum latency. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:062103. [PMID: 25019721 DOI: 10.1103/physreve.89.062103] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2014] [Indexed: 06/03/2023]
Abstract
We study the physics of quantum phase transitions from the perspective of nonequilibrium thermodynamics. For first-order quantum phase transitions, we find that the average work done per quench in crossing the critical point is discontinuous. This leads us to introduce the quantum latent work in analogy with the classical latent heat of first order classical phase transitions. For second order quantum phase transitions the irreversible work is closely related to the fidelity susceptibility for weak sudden quenches of the system Hamiltonian. We demonstrate our ideas with numerical simulations of first, second, and infinite order phase transitions in various spin chain models.
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Affiliation(s)
- E Mascarenhas
- Departamento de Física, Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brazil
| | - H Bragança
- Departamento de Física, Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brazil
| | - R Dorner
- Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2AZ, United Kingdom and Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - M França Santos
- Departamento de Física, Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brazil
| | - V Vedral
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom and Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543 and Department of Physics, National University of Singapore, 2 Science Drive 2, Singapore 117543
| | - K Modi
- School of Physics, Monash University, VIC 3800, Australia
| | - J Goold
- The Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste, Italy
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22
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Scaling of geometric quantum discord close to a topological phase transition. Sci Rep 2014; 4:4473. [PMID: 24667280 PMCID: PMC3966051 DOI: 10.1038/srep04473] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/10/2013] [Accepted: 03/10/2014] [Indexed: 11/08/2022] Open
Abstract
Quantum phase transition is one of the most interesting aspects in quantum many-body systems. Recently, geometric quantum discord has been introduced to signature the critical behavior of various quantum systems. However, it is well-known that topological quantum phase transition can not be described by the conventional Landau's symmetry breaking theory, and thus it is unknown that whether previous study can be applicable in this case. Here, we study the topological quantum phase transition in Kitaev's 1D p-wave spinless quantum wire model in terms of its ground state geometric quantum discord. The derivative of geometric quantum discord is nonanalytic at the critical point, in both zero temperature and finite temperature cases. The scaling behavior and the universality are verified numerically. Therefore, our results clearly show that all the key ingredients of the topological phase transition can be captured by the nearest neighbor and long-range geometric quantum discord.
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23
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24
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Peng X, Wu S, Li J, Suter D, Du J. Observation of the ground-state geometric phase in a Heisenberg XY model. PHYSICAL REVIEW LETTERS 2010; 105:240405. [PMID: 21231514 DOI: 10.1103/physrevlett.105.240405] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/29/2010] [Revised: 09/20/2010] [Indexed: 05/30/2023]
Abstract
Geometric phases play a central role in a variety of quantum phenomena, especially in condensed matter physics. Recently, it was shown that this fundamental concept exhibits a connection to quantum phase transitions where the system undergoes a qualitative change in the ground state when a control parameter in its Hamiltonian is varied. Here we report the first experimental study using the geometric phase as a topological test of quantum transitions of the ground state in a Heisenberg XY spin model. Using NMR interferometry, we measure the geometric phase for different adiabatic circuits that do not pass through points of degeneracy.
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Affiliation(s)
- Xinhua Peng
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China.
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25
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Quan HT, Cucchietti FM. Quantum fidelity and thermal phase transitions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:031101. [PMID: 19391896 DOI: 10.1103/physreve.79.031101] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/08/2008] [Revised: 11/11/2008] [Indexed: 05/27/2023]
Abstract
We study the quantum fidelity approach to characterize thermal phase transitions. Specifically, we focus on the mixed-state fidelity induced by a perturbation in temperature. We consider the behavior of fidelity in two types of second-order thermal phase transitions (based on the type of nonanaliticity of free energy), and we find that usual fidelity criteria for identifying critical points is more applicable to the case of lambda transitions (divergent second derivatives of free energy). Our study also reveals that for fixed perturbations, the sensitivity of fidelity at high temperatures (where thermal fluctuations wash out information about the transition) is reduced. From the connection to thermodynamical quantities we propose slight variations to the usual fidelity approach that allow us to overcome these limitations. In all cases we find that fidelity remains a good precriterion for testing thermal phase transitions, and we use it to analyze the nonzero temperature phase diagram of the Lipkin-Meshkov-Glick model.
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Affiliation(s)
- H T Quan
- Theoretical Division, MS B213, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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26
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Cummings AW, Akis R, Ferry DK. Subband anticrossing and the spin Hall effect in quantum wires. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2009; 21:055502. [PMID: 21817304 DOI: 10.1088/0953-8984/21/5/055502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We report on numerical simulations of the intrinsic spin Hall effect in semiconductor quantum wires as a function of the Rashba spin-orbit coupling strength, the electron density, and the width of the wire. We find that the strength of the spin Hall effect does not depend monotonically on these parameters, but instead exhibits a local maximum. This behavior is explained by considering the dispersion relation of the electrons in the wire, which is characterized by the anticrossing of adjacent subbands. These results lead to a simple estimate of the optimal wire width for spin Hall transport experiments, and simulations indicate that this optimal width is independent of disorder. The anticrossing of adjacent subbands is related to a quantum phase transition in momentum space, and is accompanied by an enhancement of the Berry curvature and subsequently in the magnitude of the spin Hall effect.
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Affiliation(s)
- A W Cummings
- Department of Electrical Engineering and Center for Solid State Electronics Research, Arizona State University, Tempe, AZ 85287-5706, USA
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27
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Nesterov AI, Ovchinnikov SG. Geometric phases and quantum phase transitions in open systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:015202. [PMID: 18764008 DOI: 10.1103/physreve.78.015202] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/13/2007] [Revised: 04/18/2008] [Indexed: 05/26/2023]
Abstract
The relationship is established between quantum phase transitions and complex geometric phases for open quantum systems governed by a non-Hermitian effective Hamiltonian with accidental crossing of the eigenvalues. In particular, the geometric phase associated with the ground state of the one-dimensional dissipative Ising model in a transverse magnetic field is evaluated, and it is demonstrated that the related quantum phase transition is of the first order.
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Affiliation(s)
- Alexander I Nesterov
- Departamento de Física, CUCEI, Universidad de Guadalajara, Av. Revolución 1500, Guadalajara, Codigo Postal 44420, Jalisco, México.
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28
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Paunković N, Rocha Vieira V. Macroscopic distinguishability between quantum states defining different phases of matter: fidelity and the Uhlmann geometric phase. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:011129. [PMID: 18351840 DOI: 10.1103/physreve.77.011129] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2007] [Indexed: 05/26/2023]
Abstract
We study the fidelity approach to quantum phase transitions (QPTs) and apply it to general thermal phase transitions (PTs). We analyze two particular cases: The Stoner-Hubbard itinerant electron model of magnetism and the BCS theory of superconductivity. In both cases we show that the sudden drop of the mixed state fidelity marks the line of the phase transition. We conduct a detailed analysis of the general case of systems given by mutually commuting Hamiltonians, where the nonanalyticity of the fidelity is directly related to the nonanalyticity of the relevant response functions (susceptibility and heat capacity), for the case of symmetry-breaking transitions. Further, on the case of BCS theory of superconductivity, given by mutually noncommuting Hamiltonians, we analyze the structure of the system's eigenvectors in the vicinity of the line of the phase transition showing that their sudden change is quantified by the emergence of a generically nontrivial Uhlmann mixed state geometric phase.
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Affiliation(s)
- Nikola Paunković
- SQIG-Instituto de Telecomunicações, IST, Lisbon, P-1049-001 Lisbon, Portugal
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29
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Zanardi P, Giorda P, Cozzini M. Information-theoretic differential geometry of quantum phase transitions. PHYSICAL REVIEW LETTERS 2007; 99:100603. [PMID: 17930382 DOI: 10.1103/physrevlett.99.100603] [Citation(s) in RCA: 74] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2007] [Indexed: 05/25/2023]
Abstract
The manifold of coupling constants parametrizing a quantum Hamiltonian is equipped with a natural Riemannian metric with an operational distinguishability content. We argue that the singularities of this metric are in correspondence with the quantum phase transitions featured by the corresponding system. This approach provides a universal conceptual framework to study quantum critical phenomena which is differential geometric and information theoretic at the same time.
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Affiliation(s)
- Paolo Zanardi
- Department of Physics and Astronomy, University of Southern California Los Angeles, California 90089-0484, USA
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30
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Campos Venuti L, Zanardi P. Quantum critical scaling of the geometric tensors. PHYSICAL REVIEW LETTERS 2007; 99:095701. [PMID: 17931018 DOI: 10.1103/physrevlett.99.095701] [Citation(s) in RCA: 76] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2007] [Indexed: 05/25/2023]
Abstract
Berry phases and the quantum-information theoretic notion of fidelity have been recently used to analyze quantum phase transitions from a geometrical perspective. In this Letter we unify these two approaches showing that the underlying mechanism is the critical singular behavior of a complex tensor over the Hamiltonian parameter space. This is achieved by performing a scaling analysis of this quantum geometric tensor in the vicinity of the critical points. In this way most of the previous results are understood on general grounds and new ones are found. We show that criticality is not a sufficient condition to ensure superextensive divergence of the geometric tensor, and state the conditions under which this is possible. The validity of this analysis is further checked by exact diagonalization of the spin-1/2 XXZ Heisenberg chain.
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Affiliation(s)
- Lorenzo Campos Venuti
- Institute for Scientific Interchange, Villa Gualino, Viale Settimio Severo 65, I-10133 Torino, Italy
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31
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Reuter ME, Hartmann MJ, Plenio MB. Geometric phases and critical phenomena in a chain of interacting spins. Proc Math Phys Eng Sci 2007. [DOI: 10.1098/rspa.2007.1822] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
The geometric phase can act as a signature for critical regions of interacting spin chains in the limit where the corresponding circuit in parameter space is shrunk to a point and the number of spins is extended to infinity; for finite circuit radii or finite spin chain lengths, the geometric phase is always trivial (a multiple of 2
π
). In this work, two related signatures of criticality are proposed which obey finite-size scaling and which circumvent the need for assuming any unphysical limits. They are based on the notion of the Bargmann invariant, whose phase may be regarded as a discretized version of the Berry phase. As circuits are considered which are composed of a discrete finite set of vertices in parameter space, they are able to pass directly
through
a critical point, rather than having to circumnavigate it. The proposed mechanism is shown to provide a diagnostic tool for criticality in the case of a given non-solvable one-dimensional spin chain with nearest-neighbour interactions in the presence of an external magnetic field.
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Affiliation(s)
- Moritz E Reuter
- Institute for Mathematical Sciences, Imperial College London53 Exhibition Road, London SW7 2BW, UK
| | - Michael J Hartmann
- Institute for Mathematical Sciences, Imperial College London53 Exhibition Road, London SW7 2BW, UK
| | - Martin B Plenio
- Institute for Mathematical Sciences, Imperial College London53 Exhibition Road, London SW7 2BW, UK
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32
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Pachos JK, Carollo ACM. Geometric phases and criticality in spin systems. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2006; 364:3463-76. [PMID: 17090470 DOI: 10.1098/rsta.2006.1894] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
A general formalism of the relation between geometric phases produced by circularly evolving interacting spin systems and their criticality behaviour is presented. This opens up the way for the use of geometric phases as a tool to probe regions of criticality without having to undergo a quantum phase transition. As a concrete example, a spin-1/2 chain with XY interactions is considered and the corresponding geometric phases are analysed. Finally, a generalization of these results to the case of an arbitrary spin system is presented.
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Affiliation(s)
- Jiannis K Pachos
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK.
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33
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Zanardi P, Paunković N. Ground state overlap and quantum phase transitions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:031123. [PMID: 17025610 DOI: 10.1103/physreve.74.031123] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/09/2006] [Revised: 05/31/2006] [Indexed: 05/12/2023]
Abstract
We present a characterization of quantum phase transitions in terms of the the overlap function between two ground states obtained for two different values of external parameters. On the examples of the Dicke and XY models, we show that the regions of criticality of a system are marked by the extremal points of the overlap and functions closely related to it. Further, we discuss the connections between this approach and the Anderson orthogonality catastrophe as well as with the dynamical study of the Loschmidt echo for critical systems.
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Affiliation(s)
- Paolo Zanardi
- Institute for Scientific Interchange (ISI), Villa Gualino, Viale Settimio Severo 65, I-10133 Torino, Italy
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