1
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Siovitz I, Lannig S, Deller Y, Strobel H, Oberthaler MK, Gasenzer T. Universal Dynamics of Rogue Waves in a Quenched Spinor Bose Condensate. PHYSICAL REVIEW LETTERS 2023; 131:183402. [PMID: 37977625 DOI: 10.1103/physrevlett.131.183402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2023] [Accepted: 10/10/2023] [Indexed: 11/19/2023]
Abstract
Isolated many-body systems far from equilibrium may exhibit scaling dynamics with universal exponents indicating the proximity of the time evolution to a nonthermal fixed point. We find universal dynamics connected with the occurrence of extreme wave excitations in the mutually coupled magnetic components of a spinor gas which propagate in an effectively random potential. The frequency of these rogue waves is affected by the time-varying spatial correlation length of the potential, giving rise to an additional exponent δ_{c}≃1/3 for temporal scaling, which is different from the exponent β_{V}≃1/4 characterizing the scaling of the correlation length ℓ_{V}∼t^{β_{V}} in time. As a result of the caustics, i.e., focusing events, real-time instanton defects appear in the Larmor phase of the spin-1 system as vortices in space and time. The temporal correlations governing the instanton occurrence frequency scale as t^{δ_{I}}. This suggests that the universality class of a nonthermal fixed point could be characterized by different, mutually related exponents defining the evolution in time and space, respectively. Our results have a strong relevance for understanding pattern coarsening from first principles and potential implications for dynamics ranging from the early Universe to geophysical dynamics and microphysics.
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Affiliation(s)
- Ido Siovitz
- Kirchhoff-Institut für Physik, Ruprecht-Karls Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Stefan Lannig
- Kirchhoff-Institut für Physik, Ruprecht-Karls Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Yannick Deller
- Kirchhoff-Institut für Physik, Ruprecht-Karls Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Helmut Strobel
- Kirchhoff-Institut für Physik, Ruprecht-Karls Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Markus K Oberthaler
- Kirchhoff-Institut für Physik, Ruprecht-Karls Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Thomas Gasenzer
- Kirchhoff-Institut für Physik, Ruprecht-Karls Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
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2
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Giachetti G, Defenu N. Entanglement propagation and dynamics in non-additive quantum systems. Sci Rep 2023; 13:12388. [PMID: 37524738 PMCID: PMC10390585 DOI: 10.1038/s41598-023-37984-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2023] [Accepted: 06/30/2023] [Indexed: 08/02/2023] Open
Abstract
The prominent collective character of long-range interacting quantum systems makes them promising candidates for quantum technological applications. Yet, lack of additivity overthrows the traditional picture for entanglement scaling and transport, due to the breakdown of the common mechanism based on excitations propagation and confinement. Here, we describe the dynamics of the entanglement entropy in many-body quantum systems with a diverging contribution to the internal energy from the long-range two body potential. While in the strict thermodynamic limit entanglement dynamics is shown to be suppressed, a rich mosaic of novel scaling regimes is observed at intermediate system sizes, due to the possibility to trigger multiple resonant modes in the global dynamics. Quantitative predictions on the shape and timescales of entanglement propagation are made, paving the way to the observation of these phases in current quantum simulators. This picture is connected and contrasted with the case of local many body systems subject to Floquet driving.
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Affiliation(s)
- Guido Giachetti
- SISSA and INFN Sezione di Trieste, Via Bonomea 265, 34136, Trieste, Italy
| | - Nicolò Defenu
- Institut für Theoretische Physik, ETH Zürich, Wolfgang-Pauli-Str. 27, Zurich, Switzerland.
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3
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Marino J, Eckstein M, Foster MS, Rey AM. Dynamical phase transitions in the collisionless pre-thermal states of isolated quantum systems: theory and experiments. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2022; 85:116001. [PMID: 36075190 DOI: 10.1088/1361-6633/ac906c] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2022] [Accepted: 09/08/2022] [Indexed: 06/15/2023]
Abstract
We overview the concept of dynamical phase transitions (DPTs) in isolated quantum systems quenched out of equilibrium. We focus on non-equilibrium transitions characterized by an order parameter, which features qualitatively distinct temporal behavior on the two sides of a certain dynamical critical point. DPTs are currently mostly understood as long-lived prethermal phenomena in a regime where inelastic collisions are incapable to thermalize the system. The latter enables the dynamics to substain phases that explicitly break detailed balance and therefore cannot be encompassed by traditional thermodynamics. Our presentation covers both cold atoms as well as condensed matter systems. We revisit a broad plethora of platforms exhibiting pre-thermal DPTs, which become theoretically tractable in a certain limit, such as for a large number of particles, large number of order parameter components, or large spatial dimension. The systems we explore include, among others, quantum magnets with collective interactions,ϕ4quantum field theories, and Fermi-Hubbard models. A section dedicated to experimental explorations of DPTs in condensed matter and AMO systems connects this large variety of theoretical models.
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Affiliation(s)
- Jamir Marino
- Institut für Physik, Johannes Gutenberg-Universität Mainz, D-55099 Mainz, Germany
| | - Martin Eckstein
- Department of Physics, University of Erlangen-Nürnberg, 91058 Erlangen, Germany
| | - Matthew S Foster
- Department of Physics and Astronomy, Rice University, Houston, TX 77005, United States of America
- Rice Center for Quantum Materials, Rice University, Houston, TX 77005, United States of America
| | - Ana Maria Rey
- JILA, National Institute of Standards and Technology, and Department of Physics,University of Colorado, Boulder, CO 80309, United States of America
- Center for Theory of Quantum Matter, University of Colorado, Boulder, CO 80309, United States of America
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4
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Far-from-equilibrium universality in the two-dimensional Heisenberg model. Proc Natl Acad Sci U S A 2022; 119:e2122599119. [PMID: 35787047 PMCID: PMC9282433 DOI: 10.1073/pnas.2122599119] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023] Open
Abstract
We characterize the universal far-from-equilibrium dynamics of the two-dimensional quantum Heisenberg magnet isolated from its environment. For a broad range of initial conditions, we find a long-lived universal prethermal regime characterized by self-similar behavior of spin-spin correlations. We analytically derive the spatial-temporal scaling exponents and find excellent agreement with numerics using phase space methods. The scaling exponents are insensitive to the choice of initial conditions, which include coherent and incoherent spin states with values of total magnetization and energy in a wide range. Compared to previously studied self-similar dynamics in nonequilibrium O(n) field theories and Bose gases, we find qualitatively distinct scaling behavior originating from the presence of spin modes that remain gapless at long times and are protected by the global SU(2) symmetry. Our predictions, which suggest a distinct nonequilibrium universality class from Bose gases and O(n) theories, are readily testable in ultracold atoms simulators of Heisenberg magnets.
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5
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Halimeh JC, Maghrebi MF. Quantum aging and dynamical universality in the long-range O(N→∞) model. Phys Rev E 2021; 103:052142. [PMID: 34134217 DOI: 10.1103/physreve.103.052142] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2020] [Accepted: 04/29/2021] [Indexed: 11/07/2022]
Abstract
Quantum quenches to or near criticality give rise to the phenomenon of aging, manifested by glassylike dynamics at short times and far from equilibrium. The recent surge of interest in the dynamics of quantum many-body systems has rejuvenated interest in this phenomenon. Motivated by the ubiquitous long-range interactions in emerging experimental platforms, it is vital to study quantum aging in such settings. In this paper, we investigate the dynamical universality and aging in the d-dimensional O(N) model with the long-range coupling 1/x^{d+σ} and in the mean-field limit N→∞ that allows an exact treatment. An immediate consequence of long-range coupling is the emergence of nonlinear light cones. We focus on the correlation and response functions, and identify a rich scaling behavior depending on how the corresponding space-time positions are located relative to each other, via a local light cone, and to the time of the quench via a global quench light cone. We determine the initial-slip exponent that governs the short-time dependence of two-point functions. We highlight the qualitative features of aging due to the long-range coupling, in particular in the region outside the light cones. As an important consequence of long-range coupling, the correlation function decays as 1/x^{d+σ} outside the quench light cone while increasing polynomially with the total time after quench. This is while, for short-time differences, the two-time response function "equilibrates" at all distances even outside this light cone. Our analytic findings are in excellent agreement with exact numerics, and provide a useful benchmark for modern experimental platforms with long-range interactions.
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Affiliation(s)
- Jad C Halimeh
- INO-CNR BEC Center and Department of Physics, University of Trento, Via Sommarive 14, I-38123 Trento, Italy.,Kirchhoff Institute for Physics, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany.,Institute for Theoretical Physics, Ruprecht-Karls-Universität Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
| | - Mohammad F Maghrebi
- Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
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6
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Wald S, Böttcher L. From classical to quantum walks with stochastic resetting on networks. Phys Rev E 2021; 103:012122. [PMID: 33601601 DOI: 10.1103/physreve.103.012122] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2020] [Accepted: 12/14/2020] [Indexed: 11/07/2022]
Abstract
Random walks are fundamental models of stochastic processes with applications in various fields, including physics, biology, and computer science. We study classical and quantum random walks under the influence of stochastic resetting on arbitrary networks. Based on the mathematical formalism of quantum stochastic walks, we provide a framework of classical and quantum walks whose evolution is determined by graph Laplacians. We study the influence of quantum effects on the stationary and long-time average probability distribution by interpolating between the classical and quantum regime. We compare our analytical results on stationary and long-time average probability distributions with numerical simulations on different networks, revealing differences in the way resets affect the sampling properties of classical and quantum walks.
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Affiliation(s)
- Sascha Wald
- Max-Planck-Institut für Physik Komplexer Systeme, Nöthnitzer Straße 38, D-01187 Dresden, Germany
| | - Lucas Böttcher
- Department of Computational Medicine, University of California, Los Angeles, California 90024, USA.,Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland.,Center of Economic Research, ETH Zurich, 8092 Zurich, Switzerland
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7
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Christiansen H, Majumder S, Henkel M, Janke W. Aging in the Long-Range Ising Model. PHYSICAL REVIEW LETTERS 2020; 125:180601. [PMID: 33196262 DOI: 10.1103/physrevlett.125.180601] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2019] [Revised: 08/01/2020] [Accepted: 09/10/2020] [Indexed: 06/11/2023]
Abstract
The current understanding of aging phenomena is mainly confined to the study of systems with short-ranged interactions. Little is known about the aging of long-ranged systems. Here, the aging in the phase-ordering kinetics of the two-dimensional Ising model with power-law long-range interactions is studied via Monte Carlo simulations. The dynamical scaling of the two-time spin-spin autocorrelator is well described by simple aging for all interaction ranges studied. The autocorrelation exponents are consistent with λ=1.25 in the effectively short-range regime, while for stronger long-range interactions the data are consistent with λ=d/2=1. For very long-ranged interactions, strong finite-size effects are observed. We discuss whether such finite-size effects could be misinterpreted phenomenologically as subaging.
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Affiliation(s)
- Henrik Christiansen
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany
| | - Suman Majumder
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany
| | - Malte Henkel
- Laboratoire de Physique et Chimie Théoriques (CNRS UMR 7019), Université de Lorraine Nancy, 54506 Vandœuvre-lès-Nancy Cedex, France
- Centro de Física Teórica e Computacional, Universidade de Lisboa, 1749-016 Lisboa, Portugal
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany
| | - Wolfhard Janke
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany
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8
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Jian SK, Yin S, Swingle B. Universal Prethermal Dynamics in Gross-Neveu-Yukawa Criticality. PHYSICAL REVIEW LETTERS 2019; 123:170606. [PMID: 31702242 DOI: 10.1103/physrevlett.123.170606] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/12/2019] [Indexed: 06/10/2023]
Abstract
We study the prethermal dynamics of the Gross-Neveu-Yukawa quantum field theory, suddenly quenched in the vicinity of a critical point. We find that the universal prethermal dynamics is controlled by two fixed points depending on the size of the quench. Besides the usual equilibrium chiral Ising fixed point for a shallow quench, a dynamical chiral Ising fixed point is identified for a deep quench. Intriguingly, the latter is a nonthermal fixed point without any equilibrium counterpart due to the participation of gapless fermionic fields. We also find that in the scaling regime controlled by the equilibrium fixed point, the initial slip exponent is rendered negative if there are enough flavors of fermions, thus providing a unique signature of fermionic prethermal dynamics. We then explore the temporal crossover between the universal scaling regimes governed by the two universality classes. Possible experimental realizations are also discussed.
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Affiliation(s)
- Shao-Kai Jian
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
- Condensed Matter Theory Center, Department of Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Shuai Yin
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
- School of physics, Sun Yat-Sen University, Guangzhou 510275, China
| | - Brian Swingle
- Condensed Matter Theory Center, Maryland Center for Fundamental Physics, Joint Center for Quantum Information and Computer Science, and Department of Physics, University of Maryland, College Park, Maryland 20742, USA
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9
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Lang J, Frank B, Halimeh JC. Dynamical Quantum Phase Transitions: A Geometric Picture. PHYSICAL REVIEW LETTERS 2018; 121:130603. [PMID: 30312040 DOI: 10.1103/physrevlett.121.130603] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/15/2018] [Revised: 08/01/2018] [Indexed: 06/08/2023]
Abstract
The Loschmidt echo is a purely quantum-mechanical quantity whose determination for large quantum many-body systems requires an exceptionally precise knowledge of all eigenstates and eigenenergies. One might therefore be tempted to dismiss the applicability of any approximations to the underlying time evolution as hopeless. However, using the fully connected transverse-field Ising model as an example, we show that this indeed is not the case and that a simple semiclassical approximation to systems well described by mean-field theory is, in fact, in good quantitative agreement with the exact quantum-mechanical calculation. Beyond the potential to capture the entire dynamical phase diagram of these models, the method presented here also allows for an intuitive geometric interpretation of the fidelity return rate at any temperature, thereby connecting the order parameter dynamics and the Loschmidt echo in a common framework. Videos of the postquench dynamics provided in Supplemental Material visualize this new point of view.
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Affiliation(s)
- Johannes Lang
- Physik Department, Technische Universität München, 85747 Garching, Germany
| | - Bernhard Frank
- Physik Department, Technische Universität München, 85747 Garching, Germany
| | - Jad C Halimeh
- Physik Department, Technische Universität München, 85747 Garching, Germany
- Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
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10
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Lerose A, Marino J, Žunkovič B, Gambassi A, Silva A. Chaotic Dynamical Ferromagnetic Phase Induced by Nonequilibrium Quantum Fluctuations. PHYSICAL REVIEW LETTERS 2018; 120:130603. [PMID: 29694194 DOI: 10.1103/physrevlett.120.130603] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2017] [Revised: 12/22/2017] [Indexed: 06/08/2023]
Abstract
We investigate the robustness of a dynamical phase transition against quantum fluctuations by studying the impact of a ferromagnetic nearest-neighbor spin interaction in one spatial dimension on the nonequilibrium dynamical phase diagram of the fully connected quantum Ising model. In particular, we focus on the transient dynamics after a quantum quench and study the prethermal state via a combination of analytic time-dependent spin wave theory and numerical methods based on matrix product states. We find that, upon increasing the strength of the quantum fluctuations, the dynamical critical point fans out into a chaotic dynamical phase within which the asymptotic ordering is characterized by strong sensitivity to the parameters and initial conditions. We argue that such a phenomenon is general, as it arises from the impact of quantum fluctuations on the mean-field out of equilibrium dynamics of any system which exhibits a broken discrete symmetry.
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Affiliation(s)
- Alessio Lerose
- SISSA-International School for Advanced Studies, via Bonomea 265, I-34136 Trieste, Italy
- INFN-Istituto Nazionale di Fisica Nucleare, Sezione di Trieste, I-34136 Trieste, Italy
| | - Jamir Marino
- Institut für Theoretische Physik, Universität zu Köln, D-50937 Cologne, Germany
| | - Bojan Žunkovič
- Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
| | - Andrea Gambassi
- SISSA-International School for Advanced Studies, via Bonomea 265, I-34136 Trieste, Italy
- INFN-Istituto Nazionale di Fisica Nucleare, Sezione di Trieste, I-34136 Trieste, Italy
| | - Alessandro Silva
- SISSA-International School for Advanced Studies, via Bonomea 265, I-34136 Trieste, Italy
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11
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Karl M, Cakir H, Halimeh JC, Oberthaler MK, Kastner M, Gasenzer T. Universal equilibrium scaling functions at short times after a quench. Phys Rev E 2017; 96:022110. [PMID: 28950605 DOI: 10.1103/physreve.96.022110] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2017] [Indexed: 06/07/2023]
Abstract
By analyzing spin-spin correlation functions at relatively short distances, we show that equilibrium near-critical properties can be extracted at short times after quenches into the vicinity of a quantum critical point. The time scales after which equilibrium properties can be extracted are sufficiently short so that the proposed scheme should be viable for quantum simulators of spin models based on ultracold atoms or trapped ions. Our results, analytic as well as numeric, are for one-dimensional spin models, either integrable or nonintegrable, but we expect our conclusions to be valid in higher dimensions as well.
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Affiliation(s)
- Markus Karl
- Kirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Halil Cakir
- Kirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Jad C Halimeh
- Physics Department and Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, D-80333 München, Germany
| | - Markus K Oberthaler
- Kirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Michael Kastner
- National Institute for Theoretical Physics (NITheP), Stellenbosch 7600, South Africa
- Department of Physics, Institute of Theoretical Physics, University of Stellenbosch, Stellenbosch 7600, South Africa
| | - Thomas Gasenzer
- Kirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
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12
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Foini L, Gambassi A, Konik R, Cugliandolo LF. Measuring effective temperatures in a generalized Gibbs ensemble. Phys Rev E 2017; 95:052116. [PMID: 28618551 DOI: 10.1103/physreve.95.052116] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2016] [Indexed: 06/07/2023]
Abstract
The local physical properties of an isolated quantum statistical system in the stationary state reached long after a quench are generically described by the Gibbs ensemble, which involves only its Hamiltonian and the temperature as a parameter. If the system is instead integrable, additional quantities conserved by the dynamics intervene in the description of the stationary state. The resulting generalized Gibbs ensemble involves a number of temperature-like parameters, the determination of which is practically difficult. Here we argue that in a number of simple models these parameters can be effectively determined by using fluctuation-dissipation relationships between response and correlation functions of natural observables, quantities which are accessible in experiments.
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Affiliation(s)
- Laura Foini
- Department of Quantum Matter Physics, University of Geneva, 24 Quai Ernest-Ansermet, CH-1211 Geneva, Switzerland
- Laboratoire de Physique Statistique, Département de l'ENS, École Normale Supérieure, PSL Research University, Université Paris Diderot, Sorbonne Paris Cité, Sorbonne Universités, UPMC Univ. Paris 06, CNRS, 75005 Paris, France
| | - Andrea Gambassi
- SISSA-International School for Advanced Studies and INFN, via Bonomea 265, 34136 Trieste, Italy
| | - Robert Konik
- CMPMS Division, Brookhaven National Laboratory, Building 734, Upton, New York 11973, USA
| | - Leticia F Cugliandolo
- Sorbonne Universités, Université Pierre et Marie Curie-Paris 6, Laboratoire de Physique Théorique et Hautes Energies, 4, Place Jussieu, Tour 13, 5ème étage, 75252 Paris Cedex 05, France
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13
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Weidinger SA, Knap M. Floquet prethermalization and regimes of heating in a periodically driven, interacting quantum system. Sci Rep 2017; 7:45382. [PMID: 28368025 PMCID: PMC5377259 DOI: 10.1038/srep45382] [Citation(s) in RCA: 91] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2016] [Accepted: 02/27/2017] [Indexed: 11/08/2022] Open
Abstract
We study the regimes of heating in the periodically driven O(N)-model, which is a well established model for interacting quantum many-body systems. By computing the absorbed energy with a non-equilibrium Keldysh Green's function approach, we establish three dynamical regimes: at short times a single-particle dominated regime, at intermediate times a stable Floquet prethermal regime in which the system ceases to absorb, and at parametrically late times a thermalizing regime. Our simulations suggest that in the thermalizing regime the absorbed energy grows algebraically in time with an exponent that approaches the universal value of 1/2, and is thus significantly slower than linear Joule heating. Our results demonstrate the parametric stability of prethermal states in a many-body system driven at frequencies that are comparable to its microscopic scales. This paves the way for realizing exotic quantum phases, such as time crystals or interacting topological phases, in the prethermal regime of interacting Floquet systems.
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Affiliation(s)
- Simon A. Weidinger
- Department of Physics, Walter Schottky Institute, and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany
| | - Michael Knap
- Department of Physics, Walter Schottky Institute, and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany
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14
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Chiocchetta A, Gambassi A, Diehl S, Marino J. Dynamical Crossovers in Prethermal Critical States. PHYSICAL REVIEW LETTERS 2017; 118:135701. [PMID: 28409986 DOI: 10.1103/physrevlett.118.135701] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/06/2016] [Indexed: 06/07/2023]
Abstract
We study the prethermal dynamics of an interacting quantum field theory with an N-component order parameter and O(N) symmetry, suddenly quenched in the vicinity of a dynamical critical point. Depending on the initial conditions, the evolution of the order parameter, and of the response and correlation functions, can exhibit a temporal crossover between universal dynamical scaling regimes governed, respectively, by a quantum and a classical prethermal fixed point, as well as a crossover from a Gaussian to a non-Gaussian prethermal dynamical scaling. Together with a recent experiment, this suggests that quenches may be used in order to explore the rich variety of dynamical critical points occurring in the nonequilibrium dynamics of a quantum many-body system. We illustrate this fact by using a combination of renormalization group techniques and a nonperturbative large-N limit.
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Affiliation(s)
- Alessio Chiocchetta
- Institut für Theoretische Physik, Universität zu Köln, D-50937 Cologne, Germany
- SISSA-International School for Advanced Studies and INFN, via Bonomea 265, I-34136 Trieste, Italy
| | - Andrea Gambassi
- SISSA-International School for Advanced Studies and INFN, via Bonomea 265, I-34136 Trieste, Italy
| | - Sebastian Diehl
- Institut für Theoretische Physik, Universität zu Köln, D-50937 Cologne, Germany
| | - Jamir Marino
- Institut für Theoretische Physik, Universität zu Köln, D-50937 Cologne, Germany
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15
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Blaß B, Rieger H. Test of quantum thermalization in the two-dimensional transverse-field Ising model. Sci Rep 2016; 6:38185. [PMID: 27905523 PMCID: PMC5131304 DOI: 10.1038/srep38185] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2016] [Accepted: 11/04/2016] [Indexed: 11/09/2022] Open
Abstract
We study the quantum relaxation of the two-dimensional transverse-field Ising model after global quenches with a real-time variational Monte Carlo method and address the question whether this non-integrable, two-dimensional system thermalizes or not. We consider both interaction quenches in the paramagnetic phase and field quenches in the ferromagnetic phase and compare the time-averaged probability distributions of non-conserved quantities like magnetization and correlation functions to the thermal distributions according to the canonical Gibbs ensemble obtained with quantum Monte Carlo simulations at temperatures defined by the excess energy in the system. We find that the occurrence of thermalization crucially depends on the quench parameters: While after the interaction quenches in the paramagnetic phase thermalization can be observed, our results for the field quenches in the ferromagnetic phase show clear deviations from the thermal system. These deviations increase with the quench strength and become especially clear comparing the shape of the thermal and the time-averaged distributions, the latter ones indicating that the system does not completely lose the memory of its initial state even for strong quenches. We discuss our results with respect to a recently formulated theorem on generalized thermalization in quantum systems.
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Affiliation(s)
- Benjamin Blaß
- Theoretical Physics, Saarland University, 66123 Saarbrücken, Germany
| | - Heiko Rieger
- Theoretical Physics, Saarland University, 66123 Saarbrücken, Germany
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