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Rylands C, Klobas K, Ares F, Calabrese P, Murciano S, Bertini B. Microscopic Origin of the Quantum Mpemba Effect in Integrable Systems. PHYSICAL REVIEW LETTERS 2024; 133:010401. [PMID: 39042790 DOI: 10.1103/physrevlett.133.010401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/20/2023] [Revised: 03/01/2024] [Accepted: 04/30/2024] [Indexed: 07/25/2024]
Abstract
The highly complicated nature of far from equilibrium systems can lead to a complete breakdown of the physical intuition developed in equilibrium. A famous example of this is the Mpemba effect, which states that nonequilibrium states may relax faster when they are further from equilibrium or, put another way, hot water can freeze faster than warm water. Despite possessing a storied history, the precise criteria and mechanisms underpinning this phenomenon are still not known. Here, we study a quantum version of the Mpemba effect that takes place in closed many-body systems with a U(1) conserved charge: in certain cases a more asymmetric initial configuration relaxes and restores the symmetry faster than a more symmetric one. In contrast to the classical case, we establish the criteria for this to occur in arbitrary integrable quantum systems using the recently introduced entanglement asymmetry. We describe the quantum Mpemba effect in such systems and relate the properties of the initial state, specifically its charge fluctuations, to the criteria for its occurrence. These criteria are expounded using exact analytic and numerical techniques in several examples, a free fermion model, the Rule 54 cellular automaton, and the Lieb-Liniger model.
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Affiliation(s)
- Colin Rylands
- SISSA and INFN Sezione di Trieste, via Bonomea 265, 34136 Trieste, Italy
| | - Katja Klobas
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Filiberto Ares
- SISSA and INFN Sezione di Trieste, via Bonomea 265, 34136 Trieste, Italy
| | - Pasquale Calabrese
- SISSA and INFN Sezione di Trieste, via Bonomea 265, 34136 Trieste, Italy
- International Centre for Theoretical Physics (ICTP), Strada Costiera 11, 34151 Trieste, Italy
| | - Sara Murciano
- Walter Burke Institute for Theoretical Physics, Caltech, Pasadena, California 91125, USA
- Department of Physics and IQIM, Caltech, Pasadena, California 91125, USA
| | - Bruno Bertini
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
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2
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Bertini B, Calabrese P, Collura M, Klobas K, Rylands C. Nonequilibrium Full Counting Statistics and Symmetry-Resolved Entanglement from Space-Time Duality. PHYSICAL REVIEW LETTERS 2023; 131:140401. [PMID: 37862655 DOI: 10.1103/physrevlett.131.140401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/09/2023] [Accepted: 08/28/2023] [Indexed: 10/22/2023]
Abstract
Owing to its probabilistic nature, a measurement process in quantum mechanics produces a distribution of possible outcomes. This distribution-or its Fourier transform known as full counting statistics (FCS)-contains much more information than say the mean value of the measured observable, and accessing it is sometimes the only way to obtain relevant information about the system. In fact, the FCS is the limit of an even more general family of observables-the charged moments-that characterize how quantum entanglement is split in different symmetry sectors in the presence of a global symmetry. Here we consider the evolution of the FCS and of the charged moments of a U(1) charge truncated to a finite region after a global quantum quench. For large scales these quantities take a simple large-deviation form, showing two different regimes as functions of time: while for times much larger than the size of the region they approach a stationary value set by the local equilibrium state, for times shorter than region size they show a nontrivial dependence on time. We show that, whenever the initial state is also U(1) symmetric, the leading order in time of FCS and charged moments in the out-of-equilibrium regime can be determined by means of a space-time duality. Namely, it coincides with the stationary value in the system where the roles of time and space are exchanged. We use this observation to find some general properties of FCS and charged moments out of equilibrium, and to derive an exact expression for these quantities in interacting integrable models. We test this expression against exact results in the Rule 54 quantum cellular automaton and exact numerics in the XXZ spin-1/2 chain.
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Affiliation(s)
- Bruno Bertini
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Pasquale Calabrese
- SISSA and INFN Sezione di Trieste, via Bonomea 265, 34136 Trieste, Italy
- International Centre for Theoretical Physics (ICTP), Strada Costiera 11, 34151 Trieste, Italy
| | - Mario Collura
- SISSA and INFN Sezione di Trieste, via Bonomea 265, 34136 Trieste, Italy
| | - Katja Klobas
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Colin Rylands
- SISSA and INFN Sezione di Trieste, via Bonomea 265, 34136 Trieste, Italy
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Whitelam S. Comment on "Exact large deviation statistics and trajectory phase transition of a deterministic boundary driven cellular automaton". Phys Rev E 2023; 108:036105. [PMID: 37849128 DOI: 10.1103/physreve.108.036105] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2022] [Accepted: 08/04/2023] [Indexed: 10/19/2023]
Abstract
Buča et al. [Phys. Rev. E 100, 020103(R) (2019)2470-004510.1103/PhysRevE.100.020103] study the dynamical large deviations of a boundary-driven cellular automaton. They take a double limit in which first time and then space is made infinite, and interpret the resulting large-deviation singularity as evidence of a first-order phase transition and the accompanying coexistence of two distinct dynamical phases. This view is characteristic of an approach to dynamical large deviations in which time is interpreted as if it were a spatial coordinate of a thermodynamic system [Jack, Eur. Phys. J. B 93, 74 (2020)1434-602810.1140/epjb/e2020-100605-3]. Here, I argue that the large-deviation function produced in this double limit is not consistent with the basic features of the model of Buča et al. I show that a modified limiting procedure results in a nonsingular large-deviation function consistent with those features, and that neither supports the idea of coexisting dynamical phases.
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Affiliation(s)
- Stephen Whitelam
- Molecular Foundry, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, USA
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Buča B, Garrahan JP, Prosen T, Vanicat M. Reply to "Comment on 'Exact large deviation statistics and trajectory phase transition of a deterministic boundary driven cellular automaton' ". Phys Rev E 2023; 108:036106. [PMID: 37849206 DOI: 10.1103/physreve.108.036106] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2023] [Accepted: 08/04/2023] [Indexed: 10/19/2023]
Abstract
We reply to Whitelam's Comment [Phys. Rev. E 108, 036105 (2023)2470-004510.1103/PhysRevE.108.036105] on our paper [Phys. Rev. E 100, 020103(R) (2019)2470-004510.1103/PhysRevE.100.020103] where we compute the exact large deviation (LD) statistics of a wide class of observables in the rule 54 cellular automaton. Using some heuristic arguments, Whitelam states that despite the fact that the LD functions we compute display singular behavior, this is not indicative of a LD phase transition or of dynamical phase coexistence. Here, we refute this observation and confirm that the (standard) interpretation of our exact results stands.
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Affiliation(s)
- Berislav Buča
- Niels Bohr International Academy, Niels Bohr Institute, Copenhagen University, Universitetsparken 5, 2100 Copenhagen, Denmark
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Juan P Garrahan
- School of Physics and Astronomy and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Tomaž Prosen
- Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia
| | - Matthieu Vanicat
- Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia
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Teza G, Yaacoby R, Raz O. Eigenvalue Crossing as a Phase Transition in Relaxation Dynamics. PHYSICAL REVIEW LETTERS 2023; 130:207103. [PMID: 37267560 DOI: 10.1103/physrevlett.130.207103] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2022] [Accepted: 04/07/2023] [Indexed: 06/04/2023]
Abstract
When a system's parameter is abruptly changed, a relaxation toward the new equilibrium of the system follows. We show that a crossing between the second and third eigenvalues of the relaxation operator results in a singularity in the dynamics analogous to a first-order equilibrium phase transition. While dynamical phase transitions are intrinsically hard to detect in nature, here we show how this kind of transition can be observed in an experimentally feasible four-state colloidal system. Finally, analytical proof of survival in the thermodynamic limit of a many body (1D Ising) model is provided.
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Affiliation(s)
- Gianluca Teza
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Ran Yaacoby
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Oren Raz
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
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6
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Causer L, Garrahan JP, Lamacraft A. Slow dynamics and large deviations in classical stochastic Fredkin chains. Phys Rev E 2022; 106:014128. [PMID: 35974641 DOI: 10.1103/physreve.106.014128] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2022] [Accepted: 07/05/2022] [Indexed: 06/15/2023]
Abstract
The Fredkin spin chain serves as an interesting theoretical example of a quantum Hamiltonian whose ground state exhibits a phase transition between three distinct phases, one of which violates the area law. Here we consider a classical stochastic version of the Fredkin model, which can be thought of as a simple exclusion process subject to additional kinetic constraints, and study its classical stochastic dynamics. The ground-state phase transition of the quantum chain implies an equilibrium phase transition in the stochastic problem, whose properties we quantify in terms of numerical matrix product states (MPSs). The stochastic model displays slow dynamics, including power-law decaying autocorrelation functions and hierarchical relaxation processes due to exponential localization. Like in other kinetically constrained models, the Fredkin chain has a rich structure in its dynamical large deviations-which we compute accurately via numerical MPSs-including an active-inactive phase transition and a hierarchy of trajectory phases connected to particular equilibrium states of the model. We also propose, via its height field representation, a generalization of the Fredkin model to two dimensions in terms of constrained dimer coverings of the honeycomb lattice.
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Affiliation(s)
- Luke Causer
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Juan P Garrahan
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Austen Lamacraft
- TCM Group, Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom
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Krajnik Ž, Schmidt J, Pasquier V, Ilievski E, Prosen T. Exact Anomalous Current Fluctuations in a Deterministic Interacting Model. PHYSICAL REVIEW LETTERS 2022; 128:160601. [PMID: 35522513 DOI: 10.1103/physrevlett.128.160601] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/23/2022] [Accepted: 03/24/2022] [Indexed: 06/14/2023]
Abstract
We analytically compute the full counting statistics of charge transfer in a classical automaton of interacting charged particles. Deriving a closed-form expression for the moment generating function with respect to a stationary equilibrium state, we employ asymptotic analysis to infer the structure of charge current fluctuations for a continuous range of timescales. The solution exhibits several unorthodox features. Most prominently, on the timescale of typical fluctuations the probability distribution of the integrated charge current in a stationary ensemble without bias is distinctly non-Gaussian despite diffusive behavior of dynamical charge susceptibility. While inducing a charge imbalance is enough to recover Gaussian fluctuations, we find that higher cumulants grow indefinitely in time with different exponents, implying singular scaled cumulants. We associate this phenomenon with the lack of a regularity condition on moment generating functions and the onset of a dynamical critical point. In effect, the scaled cumulant generating function does not, irrespectively of charge bias, represent a faithful generating function of the scaled cumulants, yet the associated Legendre dual yields the correct large-deviation rate function. Our findings hint at novel types of dynamical universality classes in deterministic many-body systems.
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Affiliation(s)
- Žiga Krajnik
- Faculty for Mathematics and Physics, University of Ljubljana, Jadranska ulica 19, 1000 Ljubljana, Slovenia
| | - Johannes Schmidt
- Technische Universität Berlin, Institute for Theoretical Physics, Hardenbergstr. 36, D-10623 Berlin, Germany
- Bonacci GmbH, Robert-Koch-Str. 8, 50937 Cologne, Germany
| | - Vincent Pasquier
- Institut de Physique Théorique, Université Paris Saclay, CEA, CNRS UMR 3681, 91191 Gif-sur-Yvette, France
| | - Enej Ilievski
- Faculty for Mathematics and Physics, University of Ljubljana, Jadranska ulica 19, 1000 Ljubljana, Slovenia
| | - Tomaž Prosen
- Faculty for Mathematics and Physics, University of Ljubljana, Jadranska ulica 19, 1000 Ljubljana, Slovenia
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Krajnik Ž, Ilievski E, Prosen T. Absence of Normal Fluctuations in an Integrable Magnet. PHYSICAL REVIEW LETTERS 2022; 128:090604. [PMID: 35302808 DOI: 10.1103/physrevlett.128.090604] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2021] [Revised: 12/30/2021] [Accepted: 02/11/2022] [Indexed: 06/14/2023]
Abstract
We investigate dynamical fluctuations of transferred magnetization in the one-dimensional lattice Landau-Lifshitz magnet with uniaxial anisotropy, representing an emblematic model of interacting spins. We demonstrate that the structure of fluctuations in thermal equilibrium depends radically on the characteristic dynamical scale. In the ballistic regime, typical fluctuations are found to follow a normal distribution and scaled cumulants are finite. In stark contrast, on the diffusive and superdiffusive timescales, relevant, respectively, for the easy-axis and isotropic magnet at vanishing total magnetization, typical fluctuations are no longer Gaussian and, remarkably, scaled cumulants are divergent. The observed anomalous features disappear upon breaking integrability, suggesting that the absence of normal fluctuations is intimately tied to the presence of soliton modes. In a nonequilibrium setting of the isotropic magnet with weakly polarized step-profile initial state we find a slow drift of dynamical exponent from the superdiffusive towards the diffusive value.
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Affiliation(s)
- Žiga Krajnik
- Faculty for Mathematics and Physics, University of Ljubljana, Jadranska ulica 19, 1000 Ljubljana, Slovenia
| | - Enej Ilievski
- Faculty for Mathematics and Physics, University of Ljubljana, Jadranska ulica 19, 1000 Ljubljana, Slovenia
| | - Tomaž Prosen
- Faculty for Mathematics and Physics, University of Ljubljana, Jadranska ulica 19, 1000 Ljubljana, Slovenia
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9
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Wilkinson JWP, Prosen T, Garrahan JP. Exact solution of the "Rule 150" reversible cellular automaton. Phys Rev E 2022; 105:034124. [PMID: 35428052 DOI: 10.1103/physreve.105.034124] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/03/2021] [Accepted: 02/18/2022] [Indexed: 06/14/2023]
Abstract
We study the dynamics and statistics of the Rule 150 reversible cellular automaton (RCA). This is a one-dimensional lattice system of binary variables with synchronous (Floquet) dynamics that corresponds to a bulk deterministic and reversible discretized version of the kinetically constrained "exclusive one-spin facilitated" (XOR) Fredrickson-Andersen (FA) model, where the local dynamics is restricted: A site flips if and only if its adjacent sites are in different states from each other. Similar to other RCA that have been recently studied, such as Rule 54 and Rule 201, the Rule 150 RCA is integrable, however, in contrast is noninteracting: The emergent quasiparticles, which are identified by the domain walls, behave as free fermions. This property allows us to solve the model by means of matrix product ansatz. In particular, we find the exact equilibrium and nonequilibrium stationary states for systems with closed (periodic) and open (stochastic) boundaries, respectively, resolve the full spectrum of the time evolution operator and, therefore, gain access to the relaxation dynamics, and obtain the exact large deviation statistics of dynamical observables in the long-time limit.
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Affiliation(s)
- Joseph W P Wilkinson
- School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, University of Nottingham, Nottingham, NG7 2RD, United Kingdom
| | - Tomaž Prosen
- Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
| | - Juan P Garrahan
- School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, University of Nottingham, Nottingham, NG7 2RD, United Kingdom
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10
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Klobas K, Bertini B, Piroli L. Exact Thermalization Dynamics in the "Rule 54" Quantum Cellular Automaton. PHYSICAL REVIEW LETTERS 2021; 126:160602. [PMID: 33961472 DOI: 10.1103/physrevlett.126.160602] [Citation(s) in RCA: 19] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/04/2021] [Accepted: 03/03/2021] [Indexed: 06/12/2023]
Abstract
We study the out-of-equilibrium dynamics of the quantum cellular automaton known as "Rule 54." For a class of low-entangled initial states, we provide an analytic description of the effect of the global evolution on finite subsystems in terms of simple quantum channels, which gives access to the full thermalization dynamics at the microscopic level. As an example, we provide analytic formulas for the evolution of local observables and Rényi entropies. We show that, in contrast to other known examples of exactly solvable quantum circuits, Rule 54 does not behave as a simple Markovian bath on its own parts, and displays typical nonequilibrium features of interacting integrable many-body quantum systems such as finite relaxation rate and interaction-induced dressing effects. Our study provides a rare example where the full thermalization dynamics can be solved exactly at the microscopic level.
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Affiliation(s)
- Katja Klobas
- Rudolf Peierls Centre for Theoretical Physics, Clarendon Laboratory, Oxford University, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Bruno Bertini
- Rudolf Peierls Centre for Theoretical Physics, Clarendon Laboratory, Oxford University, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Lorenzo Piroli
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology, Schellingstraße 4, 80799 München, Germany
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11
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Wilkinson JWP, Klobas K, Prosen T, Garrahan JP. Exact solution of the Floquet-PXP cellular automaton. Phys Rev E 2021; 102:062107. [PMID: 33466043 DOI: 10.1103/physreve.102.062107] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2020] [Accepted: 10/30/2020] [Indexed: 11/07/2022]
Abstract
We study the dynamics of a bulk deterministic Floquet model, the Rule 201 synchronous one-dimensional reversible cellular automaton (RCA201). The system corresponds to a deterministic, reversible, and discrete version of the PXP model, whereby a site flips only if both its nearest neighbors are unexcited. We show that the RCA201 (Floquet-PXP) model exhibits ballistic propagation of interacting quasiparticles-or solitons-corresponding to the domain walls between nontrivial threefold vacuum states. Starting from the quasiparticle picture, we find the exact matrix product state form of the nonequilibrium stationary state for a range of boundary conditions, including both periodic and stochastic. We discuss further implications of the integrability of the model.
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Affiliation(s)
- Joseph W P Wilkinson
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom.,Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Katja Klobas
- Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
| | - Tomaž Prosen
- Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
| | - Juan P Garrahan
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom.,Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
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12
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Bañuls MC, Garrahan JP. Using Matrix Product States to Study the Dynamical Large Deviations of Kinetically Constrained Models. PHYSICAL REVIEW LETTERS 2019; 123:200601. [PMID: 31809110 DOI: 10.1103/physrevlett.123.200601] [Citation(s) in RCA: 25] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2019] [Indexed: 06/10/2023]
Abstract
Here we demonstrate that tensor network techniques-originally devised for the analysis of quantum many-body problems-are well suited for the detailed study of rare event statistics in kinetically constrained models (KCMs). As concrete examples, we consider the Fredrickson-Andersen and East models, two paradigmatic KCMs relevant to the modeling of glasses. We show how variational matrix product states allow us to numerically approximate-systematically and with high accuracy-the leading eigenstates of the tilted dynamical generators, which encode the large deviation statistics of the dynamics. Via this approach, we can study system sizes beyond what is possible with other methods, allowing us to characterize in detail the finite size scaling of the trajectory-space phase transition of these models, the behavior of spectral gaps, and the spatial structure and "entanglement" properties of dynamical phases. We discuss the broader implications of our results.
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Affiliation(s)
- Mari Carmen Bañuls
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, D-80799 München, Germany
| | - Juan P Garrahan
- School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, United Kindom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham, NG7 2RD, United Kingdom
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13
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Friedman AJ, Gopalakrishnan S, Vasseur R. Integrable Many-Body Quantum Floquet-Thouless Pumps. PHYSICAL REVIEW LETTERS 2019; 123:170603. [PMID: 31702243 DOI: 10.1103/physrevlett.123.170603] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/20/2019] [Revised: 09/10/2019] [Indexed: 06/10/2023]
Abstract
We construct an interacting integrable Floquet model featuring quasiparticle excitations with topologically nontrivial chiral dispersion. This model is a fully quantum generalization of an integrable classical cellular automaton. We write down and solve the Bethe equations for the generalized quantum model and show that these take on a particularly simple form that allows for an exact solution: essentially, the quasiparticles behave like interacting hard rods. The generalized thermodynamics and hydrodynamics of this model follow directly, providing an exact description of interacting chiral particles in the thermodynamic limit. Although the model is interacting, its unusually simple structure allows us to construct operators that spread with no butterfly effect; this construction does not seem possible in other interacting integrable systems. This model exemplifies a new class of exactly solvable, interacting quantum systems specific to the Floquet setting.
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Affiliation(s)
- Aaron J Friedman
- Department of Physics and Astronomy, University of California, Irvine, California 92697, USA
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
| | - Sarang Gopalakrishnan
- Department of Physics and Astronomy, CUNY College of Staten Island, Staten Island, New York 10314, USA and Physics Program and Initiative for the Theoretical Sciences, The Graduate Center, CUNY, New York, New York 10016, USA
| | - Romain Vasseur
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
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