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Zhang H, Qian Y, Niu ZX, Wang Q. Excited-state quantum phase transitions and the entropy of the work distribution in the anharmonic Lipkin-Meshkov-Glick model. Phys Rev E 2024; 109:064110. [PMID: 39021010 DOI: 10.1103/physreve.109.064110] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2023] [Accepted: 04/26/2024] [Indexed: 07/20/2024]
Abstract
Studying the implications and characterizations of the excited-state quantum phase transitions (ESQPTs) would enable us to understand various phenomena observed in quantum many-body systems. In this work, we delve into the affects and characterizations of the ESQPTs in the anharmonic Lipkin-Meshkov-Glick (LMG) model by means of the entropy of the quantum work distribution. The entropy of the work distribution measures the complexity of the work distribution and behaves as a valuable tool for analyzing nonequilibrium work statistics. We show that the entropy of the work distribution captures salient signatures of the underlying ESQPTs in the model. In particular, a detailed analysis of the scaling behavior of the entropy verifies that it not only acts as a witness of the ESQPTs but also reveals the difference between different types of ESQPTs. We further demonstrate that the work distribution entropy also behaves as a powerful tool for understanding the features and differences of ESQPTs in the energy space. Our results provide further evidence of the usefulness of the entropy of the work distribution for investigating various phase transitions in quantum many-body systems and open up a promising way for experimentally exploring the signatures of ESQPTs.
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Affiliation(s)
| | | | | | - Qian Wang
- Department of Physics, Zhejiang Normal University, Jinhua 321004, China
- CAMTP-Center for Applied Mathematics and Theoretical Physics, University of Maribor, Mladinska 3, SI-2000, Maribor, Slovenia
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2
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García-Mata I, Vergini E, Wisniacki DA. Impact of chaos on precursors of quantum criticality. Phys Rev E 2022; 104:L062202. [PMID: 35030879 DOI: 10.1103/physreve.104.l062202] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/14/2021] [Accepted: 12/09/2021] [Indexed: 11/07/2022]
Abstract
Excited-state quantum phase transitions (ESQPTs) are critical phenomena that generate singularities in the spectrum of quantum systems. For systems with a classical counterpart, these phenomena have their origin in the classical limit when the separatrix of an unstable periodic orbit divides phase space into different regions. Using a semiclassical theory of wave propagation based on the manifolds of unstable periodic orbits, we describe the quantum states associated with an ESQPT for the quantum standard map: a paradigmatic example of a kicked quantum system. Moreover, we show that finite-size precursors of ESQPTs shrink as chaos increases due to the disturbance of the system. This phenomenon is explained through destructive interference between principal homoclinic orbits.
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Affiliation(s)
- Ignacio García-Mata
- Instituto de Investigaciones Físicas de Mar del Plata, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata and CONICET, 7600 Mar del Plata, Argentina
| | - Eduardo Vergini
- Departamento de Física, Comisión Nacional de Energía Atómica, Avenida del Libertador 8250, (C1429BNP) Buenos Aires, Argentina.,Escuela de Ciencia y Tecnología, Universidad Nacional de General San Martín, Alem 3901, (B1653HIM) Villa Ballester, Argentina
| | - Diego A Wisniacki
- Departamento de Física "J. J. Giambiagi" and IFIBA, FCEyN, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
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3
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Wang Q, Pérez-Bernal F. Signatures of excited-state quantum phase transitions in quantum many-body systems: Phase space analysis. Phys Rev E 2021; 104:034119. [PMID: 34654165 DOI: 10.1103/physreve.104.034119] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2021] [Accepted: 08/31/2021] [Indexed: 11/07/2022]
Abstract
Using the Husimi quasiprobability distribution, we investigate the phase space signatures of excited-state quantum phase transitions (ESQPTs) in the Lipkin-Meshkov-Glick and coupled top models. We show that the ESQPT is evinced by the dynamics of the Husimi function, that exhibits a distinct time dependence in the different ESQPT phases. We also discuss how to identify the ESQPT signatures from the long-time averaged Husimi function and its associated marginal distributions. Moreover, from the calculated second moment and Wherl entropy of the long-time averaged Husimi function, we estimate the critical points of the ESQPT in both models, obtaining a good agreement with analytical (mean field) results. We provide a firm evidence that phase space methods are both a new probe for the detection and a valuable tool for the study of ESQPTs.
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Affiliation(s)
- Qian Wang
- Department of Physics, Zhejiang Normal University, Jinhua 321004, China and CAMTP-Center for Applied Mathematics and Theoretical Physics, University of Maribor, Mladinska 3, SI-2000 Maribor, Slovenia
| | - Francisco Pérez-Bernal
- Departamento de Ciencias Integradas y Centro de Estudios Avanzados en Física, Matemáticas y Computación, Universidad de Huelva, Huelva 21071, Spain and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Granada 18071, Spain
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4
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Corps ÁL, Relaño A. Constant of Motion Identifying Excited-State Quantum Phases. PHYSICAL REVIEW LETTERS 2021; 127:130602. [PMID: 34623829 DOI: 10.1103/physrevlett.127.130602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2021] [Revised: 07/26/2021] [Accepted: 09/03/2021] [Indexed: 06/13/2023]
Abstract
We propose that a broad class of excited-state quantum phase transitions (ESQPTs) gives rise to two different excited-state quantum phases. These phases are identified by means of an operator C[over ^], which is a constant of motion in only one of them. Hence, the ESQPT critical energy splits the spectrum into one phase where the equilibrium expectation values of physical observables crucially depend on this constant of motion and another phase where the energy is the only relevant thermodynamic magnitude. The trademark feature of this operator is that it has two different eigenvalues ±1, and, therefore, it acts as a discrete symmetry in the first of these two phases. This scenario is observed in systems with and without an additional discrete symmetry; in the first case, C[over ^] explains the change from degenerate doublets to nondegenerate eigenlevels upon crossing the critical line. We present stringent numerical evidence in the Rabi and Dicke models, suggesting that this result is exact in the thermodynamic limit, with finite-size corrections that decrease as a power law.
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Affiliation(s)
- Ángel L Corps
- Departamento de Estructura de la Materia, Física Térmica y Electrónica and Grupo Interdisciplinar de Sistemas Complejos (GISC), Universidad Complutense de Madrid, Avenida Complutense s/n, E-28040 Madrid, Spain
| | - Armando Relaño
- Departamento de Estructura de la Materia, Física Térmica y Electrónica and Grupo Interdisciplinar de Sistemas Complejos (GISC), Universidad Complutense de Madrid, Avenida Complutense s/n, E-28040 Madrid, Spain
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5
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Feldmann P, Klempt C, Smerzi A, Santos L, Gessner M. Interferometric Order Parameter for Excited-State Quantum Phase Transitions in Bose-Einstein Condensates. PHYSICAL REVIEW LETTERS 2021; 126:230602. [PMID: 34170156 DOI: 10.1103/physrevlett.126.230602] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2020] [Revised: 03/05/2021] [Accepted: 04/19/2021] [Indexed: 06/13/2023]
Abstract
Excited-state quantum phase transitions extend the notion of quantum phase transitions beyond the ground state. They are characterized by closing energy gaps amid the spectrum. Identifying order parameters for excited-state quantum phase transitions poses, however, a major challenge. We introduce a topological order parameter that distinguishes excited-state phases in a large class of mean-field models and can be accessed by interferometry in current experiments with spinor Bose-Einstein condensates. Our work opens a way for the experimental characterization of excited-state quantum phases in atomic many-body systems.
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Affiliation(s)
- Polina Feldmann
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, 30167 Hannover, Germany
| | - Carsten Klempt
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany
- Deutsches Zentrum für Luft- und Raumfahrt e.V. (DLR), Institut für Satellitengeodäsie und Inertialsensorik, c/o Leibniz Universität Hannover, DLR-SI, Callinstraße 36, 30167 Hannover, Germany
| | - Augusto Smerzi
- QSTAR, INO-CNR, and LENS, Largo Enrico Fermi 2, 50125 Firenze, Italy
| | - Luis Santos
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, 30167 Hannover, Germany
| | - Manuel Gessner
- Laboratoire Kastler Brossel, ENS-Université PSL, CNRS, Sorbonne Université, Collège de France, 24 Rue Lhomond, 75005 Paris, France
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6
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Geiger B, Urbina JD, Richter K. Emergence of a Renormalized 1/N Expansion in Quenched Critical Many-Body Systems. PHYSICAL REVIEW LETTERS 2021; 126:110602. [PMID: 33798381 DOI: 10.1103/physrevlett.126.110602] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/20/2020] [Revised: 12/14/2020] [Accepted: 02/12/2021] [Indexed: 06/12/2023]
Abstract
We consider the fate of 1/N expansions in unstable many-body quantum systems, as realized by a quench across criticality, and show the emergence of e^{2λt}/N as a renormalized parameter ruling the quantum-classical transition and accounting nonperturbatively for the local divergence rate λ of mean-field solutions. In terms of e^{2λt}/N, quasiclassical expansions of paradigmatic examples of criticality, like the self-trapping transition in an integrable Bose-Hubbard dimer and the generic instability of attractive bosonic systems toward soliton formation, are pushed to arbitrarily high orders. The agreement with numerical simulations supports the general nature of our results in the appropriately combined long-time λt→∞ quasiclassical N→∞ regime, out of reach of expansions in the bare parameter 1/N. For scrambling in many-body hyperbolic systems, our results provide formal grounds to a conjectured multiexponential form of out-of-time-ordered correlators.
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Affiliation(s)
- Benjamin Geiger
- Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
| | - Juan Diego Urbina
- Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
| | - Klaus Richter
- Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
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7
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Wang Q, Pérez-Bernal F. Characterizing the Lipkin-Meshkov-Glick model excited-state quantum phase transition using dynamical and statistical properties of the diagonal entropy. Phys Rev E 2021; 103:032109. [PMID: 33862777 DOI: 10.1103/physreve.103.032109] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2020] [Accepted: 02/17/2021] [Indexed: 06/12/2023]
Abstract
Using the diagonal entropy, we analyze the dynamical signatures of the Lipkin-Meshkov-Glick model excited-state quantum phase transition (ESQPT). We first show that the time evolution of the diagonal entropy behaves as an efficient indicator of the presence of an ESQPT. We also compute the probability distribution of the diagonal entropy values over a certain time interval and we find that the resulting distribution provides a clear distinction between the different phases of ESQPT. Moreover, we observe that the probability distribution of the diagonal entropy at the ESQPT critical point has a universal form, well described by a beta distribution, and that a reliable detection of the ESQPT can be obtained from the diagonal entropy central moments.
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Affiliation(s)
- Qian Wang
- Department of Physics, Zhejiang Normal University, Jinhua 321004, China and CAMTP-Center for Applied Mathematics and Theoretical Physics, University of Maribor, Mladinska 3, SI-2000 Maribor, Slovenia
| | - Francisco Pérez-Bernal
- Departamento de Ciencias Integradas y Centro de Estudios Avanzados en Física, Matemáticas y Computación, Universidad de Huelva, Huelva 21071, Spain and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Granada 18071, Spain
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8
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Stránský P, Šindelka M, Kloc M, Cejnar P. Complex Density of Continuum States in Resonant Quantum Tunneling. PHYSICAL REVIEW LETTERS 2020; 125:020401. [PMID: 32701313 DOI: 10.1103/physrevlett.125.020401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/10/2020] [Accepted: 06/16/2020] [Indexed: 06/11/2023]
Abstract
We introduce a complex-extended continuum level density and apply it to one-dimensional scattering problems involving tunneling through finite-range potentials. We show that the real part of the density is proportional to a real "time shift" of the transmitted particle, while the imaginary part reflects the imaginary time of an instantonlike tunneling trajectory. We confirm these assumptions for several potentials using the complex scaling method. In particular, we show that stationary points of the potentials give rise to specific singularities of both real and imaginary densities which represent close analogues of excited-state quantum phase transitions in bound systems.
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Affiliation(s)
- Pavel Stránský
- Institute of Particle and Nuclear Physics, Faculty of Mathematics and Physics, Charles University, V Holešovičkách 2, 18000 Prague, Czech Republic
| | - Milan Šindelka
- Institute of Plasma Physics, Academy of Sciences of the Czech Republic, Za Slovankou 3, 18200 Prague, Czech Republic
| | - Michal Kloc
- Institute of Particle and Nuclear Physics, Faculty of Mathematics and Physics, Charles University, V Holešovičkách 2, 18000 Prague, Czech Republic
- Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
| | - Pavel Cejnar
- Institute of Particle and Nuclear Physics, Faculty of Mathematics and Physics, Charles University, V Holešovičkách 2, 18000 Prague, Czech Republic
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9
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Classical and Quantum Signatures of Quantum Phase Transitions in a (Pseudo) Relativistic Many-Body System. CONDENSED MATTER 2020. [DOI: 10.3390/condmat5020026] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
We identify a (pseudo) relativistic spin-dependent analogue of the celebrated quantum phase transition driven by the formation of a bright soliton in attractive one-dimensional bosonic gases. In this new scenario, due to the simultaneous existence of the linear dispersion and the bosonic nature of the system, special care must be taken with the choice of energy region where the transition takes place. Still, due to a crucial adiabatic separation of scales, and identified through extensive numerical diagonalization, a suitable effective model describing the transition is found. The corresponding mean-field analysis based on this effective model provides accurate predictions for the location of the quantum phase transition when compared against extensive numerical simulations. Furthermore, we numerically investigate the dynamical exponents characterizing the approach from its finite-size precursors to the sharp quantum phase transition in the thermodynamic limit.
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10
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Hummel Q, Geiger B, Urbina JD, Richter K. Reversible Quantum Information Spreading in Many-Body Systems near Criticality. PHYSICAL REVIEW LETTERS 2019; 123:160401. [PMID: 31702378 DOI: 10.1103/physrevlett.123.160401] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2018] [Indexed: 06/10/2023]
Abstract
Quantum chaotic interacting N-particle systems are assumed to show fast and irreversible spreading of quantum information on short (Ehrenfest) time scales ∼logN. Here, we show that, near criticality, certain many-body systems exhibit fast initial scrambling, followed subsequently by oscillatory behavior between reentrant localization and delocalization of information in Hilbert space. We consider both integrable and nonintegrable quantum critical bosonic systems with attractive contact interaction that exhibit locally unstable dynamics in the corresponding many-body phase space of the large-N limit. Semiclassical quantization of the latter accounts for many-body correlations in excellent agreement with simulations. Most notably, it predicts an asymptotically constant local level spacing ℏ/τ, again given by τ∼logN. This unique timescale governs the long-time behavior of out-of-time-order correlators that feature quasiperiodic recurrences indicating reversibility.
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Affiliation(s)
- Quirin Hummel
- Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
| | - Benjamin Geiger
- Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
| | - Juan Diego Urbina
- Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
| | - Klaus Richter
- Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
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11
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Pérez-Fernández P, Relaño A. From thermal to excited-state quantum phase transition: The Dicke model. Phys Rev E 2018; 96:012121. [PMID: 29347062 DOI: 10.1103/physreve.96.012121] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/26/2016] [Indexed: 11/07/2022]
Abstract
We study the thermodynamics of the full version of the Dicke model, including all the possible values of the total angular momentum j, with both microcanonical and canonical ensembles. We focus on both the excited-state quantum phase transition, appearing in the microcanonical description of the maximum angular momentum sector, j=N/2, and the thermal phase transition, which occurs when all the sectors are taken into account. We show that two different features characterize the full version of the Dicke model. If the system is in contact with a thermal bath and is described by means of the canonical ensemble, the parity symmetry becomes spontaneously broken at the critical temperature. In the microcanonical ensemble, and despite that all the logarithmic singularities which characterize the excited-state quantum phase transition are ruled out when all the j sectors are considered, there still exists a critical energy (or temperature) dividing the spectrum into two regions: one in which the parity symmetry can be broken, and another in which this symmetry is always well defined.
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Affiliation(s)
- P Pérez-Fernández
- Departamento de Física Aplicada III, Escuela Técnica Superior de Ingeniería, Universidad de Sevilla, Sevilla, Spain
| | - A Relaño
- Departamento de Física Aplicada I and GISC, Universidad Complutense de Madrid, Avenida Complutense s/n, 28040 Madrid, Spain
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12
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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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13
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Kopylov W, Schaller G, Brandes T. Nonadiabatic dynamics of the excited states for the Lipkin-Meshkov-Glick model. Phys Rev E 2017; 96:012153. [PMID: 29347272 DOI: 10.1103/physreve.96.012153] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2017] [Indexed: 06/07/2023]
Abstract
We theoretically investigate the impact of the excited state quantum phase transition on the adiabatic dynamics for the Lipkin-Meshkov-Glick model. Using a time-dependent protocol, we continuously change a model parameter and then discuss the scaling properties of the system especially close to the excited state quantum phase transition where we find that these depend on the energy eigenstate. On top, we show that the mean-field dynamics with the time-dependent protocol gives the correct scaling and expectation values in the thermodynamic limit even for the excited states.
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Affiliation(s)
- Wassilij Kopylov
- Institut für Theoretische Physik, Technische Universität Berlin, D-10623 Berlin, Germany
| | - Gernot Schaller
- Institut für Theoretische Physik, Technische Universität Berlin, D-10623 Berlin, Germany
| | - Tobias Brandes
- Institut für Theoretische Physik, Technische Universität Berlin, D-10623 Berlin, Germany
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14
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Restrepo S, Cerrillo J, Bastidas VM, Angelakis DG, Brandes T. Driven Open Quantum Systems and Floquet Stroboscopic Dynamics. PHYSICAL REVIEW LETTERS 2016; 117:250401. [PMID: 28036226 DOI: 10.1103/physrevlett.117.250401] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/28/2016] [Indexed: 06/06/2023]
Abstract
We provide an analytic solution to the problem of system-bath dynamics under the effect of high-frequency driving that has applications in a large class of settings, such as driven-dissipative many-body systems. Our method relies on discrete symmetries of the system-bath Hamiltonian and provides the time evolution operator of the full system, including bath degrees of freedom, without weak-coupling or Markovian assumptions. An interpretation of the solution in terms of the stroboscopic evolution of a family of observables under the influence of an effective static Hamiltonian is proposed, which constitutes a flexible simulation procedure of nontrivial Hamiltonians. We instantiate the result with the study of the spin-boson model with time-dependent tunneling amplitude. We analyze the class of Hamiltonians that may be stroboscopically accessed for this example and illustrate the dynamics of system and bath degrees of freedom.
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Affiliation(s)
- S Restrepo
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany
| | - J Cerrillo
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany
| | - V M Bastidas
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
| | - D G Angelakis
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
- School of Electrical and Computer Engineering, Technical University of Crete, Chania, Crete 73100, Greece
| | - T Brandes
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany
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15
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Relaño A, Esebbag C, Dukelsky J. Excited-state quantum phase transitions in the two-spin elliptic Gaudin model. Phys Rev E 2016; 94:052110. [PMID: 27967097 DOI: 10.1103/physreve.94.052110] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2016] [Indexed: 11/07/2022]
Abstract
We study the integrability of the two-spin elliptic Gaudin model for arbitrary values of the Hamiltonian parameters. The limit of a very large spin coupled to a small one is well described by a semiclassical approximation with just one degree of freedom. Its spectrum is divided into bands that do not overlap if certain conditions are fulfilled. In spite of the fact that there are no quantum phase transitions in each of the band heads, the bands show excited-state quantum phase transitions separating a region in which the parity symmetry is broken from another region in which time-reversal symmetry is broken. We derive analytical expressions for the critical energies in the semiclassical approximation, and confirm the results by means of exact diagonalizations for large systems.
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Affiliation(s)
- Armando Relaño
- Departamento de Física Aplicada I and GISC, Universidad Complutense de Madrid, Avenida Complutense s/n, 28040 Madrid, Spain
| | - Carlos Esebbag
- Departamento de Física y Matemáticas, Universidad de Alcalá, E-28871 Alcalá de Henares, Spain
| | - Jorge Dukelsky
- Instituto de Estructura de la Materia, Consejo Superior de Investigaciones Científicas, Serrano 123, E-28006 Madrid, Spain
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16
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Bandyopadhyay JN, Guha Sarkar T. Effective time-independent analysis for quantum kicked systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:032923. [PMID: 25871188 DOI: 10.1103/physreve.91.032923] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/10/2014] [Indexed: 06/04/2023]
Abstract
We present a mapping of potentially chaotic time-dependent quantum kicked systems to an equivalent approximate effective time-independent scenario, whereby the system is rendered integrable. The time evolution is factorized into an initial kick, followed by an evolution dictated by a time-independent Hamiltonian and a final kick. This method is applied to the kicked top model. The effective time-independent Hamiltonian thus obtained does not suffer from spurious divergences encountered if the traditional Baker-Cambell-Hausdorff treatment is used. The quasienergy spectrum of the Floquet operator is found to be in excellent agreement with the energy levels of the effective Hamiltonian for a wide range of system parameters. The density of states for the effective system exhibits sharp peaklike features, pointing towards quantum criticality. The dynamics in the classical limit of the integrable effective Hamiltonian shows remarkable agreement with the nonintegrable map corresponding to the actual time-dependent system in the nonchaotic regime. This suggests that the effective Hamiltonian serves as a substitute for the actual system in the nonchaotic regime at both the quantum and classical level.
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Affiliation(s)
| | - Tapomoy Guha Sarkar
- Department of Physics, Birla Institute of Technology and Science, Pilani 333031, India
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17
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Relaño A, Dukelsky J, Pérez-Fernández P, Arias JM. Quantum phase transitions of atom-molecule Bose mixtures in a double-well potential. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:042139. [PMID: 25375470 DOI: 10.1103/physreve.90.042139] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/09/2014] [Indexed: 06/04/2023]
Abstract
The ground state and spectral properties of Bose gases in double-well potentials are studied in two different scenarios: (i) an interacting atomic Bose gas, and (ii) a mixture of an atomic gas interacting with diatomic molecules. A ground state second-order quantum phase transition is observed in both scenarios. For large attractive values of the atom-atom interaction, the ground state is degenerate. For repulsive and small attractive interaction, the ground state is not degenerate and is well approximated by a boson coherent state. Both systems depict an excited state quantum phase transition. In both cases, a critical energy separates a region in which all the energy levels are degenerate in pairs, from another region in which there are no degeneracies. For the atomic system, the critical point displays a singularity in the density of states, whereas this behavior is largely smoothed for the mixed atom-molecule system.
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Affiliation(s)
- A Relaño
- Departamento de Física Aplicada I and GISC, Universidad Complutense de Madrid, 28040 Madrid, Spain
| | - J Dukelsky
- Instituto de Estructura de la Materia, CSIC, Serrano 123, 28006 Madrid, Spain
| | - P Pérez-Fernández
- Departamento de Física Aplicada III, Universidad de Sevilla, Sevilla, Spain
| | - J M Arias
- Departamento de Física Atómica, Molecular y Nuclear, Universidad de Sevilla and Unidad Asociada to IEM (CSIC) Madrid, Spain
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