Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1802.03401 · Physical review. B./Physical review. B

Anomalous thermalization and transport in disordered interacting Floquet systems

Sthitadhi Roy, Yevgeny Bar Lev, David J. Luitz

Published Aug 7, 2018• 34 citations
arXivHTMLPDF

Abstract

Local observables in generic periodically driven closed quantum systems are known to relax to values described by periodic infinite temperature ensembles. At the same time, ergodic static systems exhibit anomalous thermalization of local observables and satisfy a modified version of the eigenstate thermalization hypothesis (ETH), when disorder is present. This raises the question, how does the introduction of disorder affect relaxation in periodically driven systems? In this Rapid Communication, we analyze this problem by numerically studying transport and thermalization in an archetypal example. We find that thermalization is anomalous and is accompanied by subdiffusive transport with a disorder-dependent dynamical exponent. Distributions of matrix elements of local operators in the eigenbases of a family of effective time-independent Hamiltonians, which describe the stroboscopic dynamics of such systems, show anomalous departures from predictions of ETH, signaling that only a modified version of ETH is satisfied. The dynamical exponent is shown to be related to the scaling of the variance of these distributions with system size.

DOI
10.1103/physrevb.98.060201

Related papers

Anomalous Thermalization in Ergodic Systems

David J. Luitz, Yevgeny Bar Lev

It is commonly believed that quantum isolated systems satisfying the eigenstate thermalization hypothesis (ETH) are diffusive. We show that this assumption is too restrictive since there are systems that are asymptotically in a thermal state yet exhibit anomalous, subdiffusive thermalization. We show that such systems satisfy a modified version of the ETH ansatz and derive a general connection between the scaling of the variance of the off-diagonal matrix elements of local operators, written in the eigenbasis of the Hamiltonian, and the dynamical exponent. We find that for subdiffusively thermalizing systems the variance scales more slowly with system size than expected for diffusive systems. We corroborate our findings by numerically studying the distribution of the coefficients of the eigenfunctions and the off-diagonal matrix elements of local operators of the random field Heisenberg chain, which has anomalous transport in its thermal phase. Surprisingly, this system also has non-Gaussian distributions of the eigenfunctions, thus, directly violating Berry's conjecture.

arXiv:1607.01012•Physical Review Letters•Oct 21, 2016•193 citations

Transport and localization in driven disordered potentials with quantum and thermal fluctuations

Anonymous, Zohra Mehri

The transport and localization of quantum droplets in time-dependent periodic disorder potentials are systematically studied. Our numerical results indicate that such exquisite periodically driven structures may support quantum phases that are principally different compared to static systems. We observe an intriguing anomalous diffusion, with a diffusion exponent depending on the strength of quantum fluctuations and on noise parameters (amplitude and frequency). We show that the interplay of quantum fluctuations and noise tends to suppress localization especially in a large droplet, while the transport is subdiffusive in a small droplet only for a very weak noise. For reducing modulation strength and at fixed dephasing time, the system may exhibit Anderson localization of the Floquet states in the small droplet. We also elucidate the role of thermal effects in the transport properties of quantum droplets. The obtained anomalous diffusion is justified in the frame of a heuristic model.

Physical Review Research•Jul 23, 2026•0 citations

Inhomogeneous Floquet thermalization

Soumya Bera, Ishita Modak, Roderich Moessner

How a closed system thermalizes, especially in the absence of global conservation laws but in the presence of disorder and interactions, is one of the central questions in nonequilibrium statistical mechanics. We explore this for a disordered, periodically driven Ising chain. Our numerical results reveal inhomogeneous thermalization leading to a distribution of thermalization timescales within a single disordered sample, which we encode via a distribution of effective local temperatures. Using this, we find an excellent collapse without any fitting parameters of the local relaxation dynamics for the entire range of disorder values in the ergodic regime when adapting the disorder-averaged diagonal entanglement entropy as internal ``time'' of the system. This approach evidences a remarkably uniform parametrization of the dynamical many-body evolution of local temperature within the otherwise highly heterogeneous ergodic regime, independent of the strength of the disorder.

arXiv:2403.08369•Physical review. B./Physical review. B•Jun 24, 2024•3 citations

Thermalization in a periodically driven fully connected quantum Ising ferromagnet

Angelo Russomanno, Rosario Fazio, Giuseppe E. Santoro

By means of a Floquet analysis, we study the quantum dynamics of a fully connected Lipkin-Ising ferromagnet in a periodically driven transverse field showing that thermalization in the steady state is intimately connected to properties of the classical Hamiltonian dynamics. When the dynamics is ergodic, the Floquet spectrum obeys a Wigner-Dyson statistics and the system satisfies the eigenstate thermalization hypothesis (ETH): Independently of the initial state, local observables relax to the thermal value, and Floquet states are delocalized in the Hilbert space. On the contrary, if the classical dynamics is regular no thermalization occurs. We further discuss the relationship between ergodicity and dynamical phase transitions, and the relevance of our results to other fully connected periodically driven models (like the Bose-Hubbard one), and possibilities of experimental realization in the case of two coupled BEC.

arXiv:1412.0202•Europhysics Letters (EPL)•May 1, 2015•44 citations

Unveiling Eigenstate Thermalization for Non-Hermitian systems

Sudipto Singha Roy, Soumik Bandyopadhyay, Ricardo Costa de Almeida +1 more

The eigenstate thermalization hypothesis (ETH) has been highly influential in explaining thermodynamic behavior of closed quantum systems. As of yet, it is unclear whether and how the ETH applies to non-Hermitian systems. Here, we introduce a framework that extends the ETH to non-Hermitian systems, within which expectation values of local operators reproduce statistical and scaling predictions known from Hermitian ETH. We illustrate the validity of the framework on non-Hermitian random-matrix and Sachdev-Ye-Kitaev models. Further, we show numerically how the static ETH predictions become imprinted onto the dynamics of local observables. Finally, we present a prescription for observing both ETH-obeying and ETH-violating regimes in an optical-lattice experiment that implements a disordered interacting Hatano-Nelson model. Our results generalize the celebrated ETH to the non-Hermitian setting, and they show how it affects the system dynamics, and how the salient signatures can be observed in present-day cold-atom experiments.

arXiv:2309.00049•Physical Review Letters•May 8, 2025•10 citations

Thermalization mechanism for time-periodic finite isolated interacting quantum systems

Dong E. Liu

We present a theory to describe thermalization mechanism for time-periodic finite isolated interacting quantum systems. The long time asymptote of natural observables in Floquet states is directly related to averages of these observables governed by a time-independent effective Hamiltonian. We prove that if the effective system is nonintegrable and satisfies eigenstate thermalization hypothesis, quantum states of such time-periodic isolated systems will thermalize. After a long time evolution, system will relax to a stationary state, which only depends on an initial energy of the effective Hamiltonian and follows a generalized eigenstate thermalization hypothesis. A numerical test for the periodically modulated Bose-Hubbard model, with the extra nearest neighbor interaction on the bosonic lattice, agrees with the theoretical predictions.

arXiv:1410.2962•Oct 11, 2014•1 citation
Local observables in generic periodically driven closed quantum systems are known to relax to values described by periodic infinite temperature ensembles. At the same time, ergodic static systems exhibit anomalous thermalization of local observables and satisfy a modified version of the eigenstate thermalization hypothesis (ETH), when disorder is present. This raises the question, how does the introduction of disorder affect relaxation in periodically driven systems? In this Rapid Communication, we analyze this problem by numerically studying transport and thermalization in an archetypal example. We find that thermalization is anomalous and is accompanied by subdiffusive transport with a disorder-dependent dynamical exponent. Distributions of matrix elements of local operators in the eigenbases of a family of effective time-independent Hamiltonians, which describe the stroboscopic dynamics of such systems, show anomalous departures from predictions of ETH, signaling that only a modified version of ETH is satisfied. The dynamical exponent is shown to be related to the scaling of the variance of these distributions with system size.
It is commonly believed that quantum isolated systems satisfying the eigenstate thermalization hypothesis (ETH) are diffusive. We show that this assumption is too restrictive since there are systems that are asymptotically in a thermal state yet exhibit anomalous, subdiffusive thermalization. We show that such systems satisfy a modified version of the ETH ansatz and derive a general connection between the scaling of the variance of the off-diagonal matrix elements of local operators, written in the eigenbasis of the Hamiltonian, and the dynamical exponent. We find that for subdiffusively thermalizing systems the variance scales more slowly with system size than expected for diffusive systems. We corroborate our findings by numerically studying the distribution of the coefficients of the eigenfunctions and the off-diagonal matrix elements of local operators of the random field Heisenberg chain, which has anomalous transport in its thermal phase. Surprisingly, this system also has non-Gaussian distributions of the eigenfunctions, thus, directly violating Berry's conjecture.
The transport and localization of quantum droplets in time-dependent periodic disorder potentials are systematically studied. Our numerical results indicate that such exquisite periodically driven structures may support quantum phases that are principally different compared to static systems. We observe an intriguing anomalous diffusion, with a diffusion exponent depending on the strength of quantum fluctuations and on noise parameters (amplitude and frequency). We show that the interplay of quantum fluctuations and noise tends to suppress localization especially in a large droplet, while the transport is subdiffusive in a small droplet only for a very weak noise. For reducing modulation strength and at fixed dephasing time, the system may exhibit Anderson localization of the Floquet states in the small droplet. We also elucidate the role of thermal effects in the transport properties of quantum droplets. The obtained anomalous diffusion is justified in the frame of a heuristic model.
How a closed system thermalizes, especially in the absence of global conservation laws but in the presence of disorder and interactions, is one of the central questions in nonequilibrium statistical mechanics. We explore this for a disordered, periodically driven Ising chain. Our numerical results reveal inhomogeneous thermalization leading to a distribution of thermalization timescales within a single disordered sample, which we encode via a distribution of effective local temperatures. Using this, we find an excellent collapse without any fitting parameters of the local relaxation dynamics for the entire range of disorder values in the ergodic regime when adapting the disorder-averaged diagonal entanglement entropy as internal ``time'' of the system. This approach evidences a remarkably uniform parametrization of the dynamical many-body evolution of local temperature within the otherwise highly heterogeneous ergodic regime, independent of the strength of the disorder.
By means of a Floquet analysis, we study the quantum dynamics of a fully connected Lipkin-Ising ferromagnet in a periodically driven transverse field showing that thermalization in the steady state is intimately connected to properties of the classical Hamiltonian dynamics. When the dynamics is ergodic, the Floquet spectrum obeys a Wigner-Dyson statistics and the system satisfies the eigenstate thermalization hypothesis (ETH): Independently of the initial state, local observables relax to the thermal value, and Floquet states are delocalized in the Hilbert space. On the contrary, if the classical dynamics is regular no thermalization occurs. We further discuss the relationship between ergodicity and dynamical phase transitions, and the relevance of our results to other fully connected periodically driven models (like the Bose-Hubbard one), and possibilities of experimental realization in the case of two coupled BEC.
The eigenstate thermalization hypothesis (ETH) has been highly influential in explaining thermodynamic behavior of closed quantum systems. As of yet, it is unclear whether and how the ETH applies to non-Hermitian systems. Here, we introduce a framework that extends the ETH to non-Hermitian systems, within which expectation values of local operators reproduce statistical and scaling predictions known from Hermitian ETH. We illustrate the validity of the framework on non-Hermitian random-matrix and Sachdev-Ye-Kitaev models. Further, we show numerically how the static ETH predictions become imprinted onto the dynamics of local observables. Finally, we present a prescription for observing both ETH-obeying and ETH-violating regimes in an optical-lattice experiment that implements a disordered interacting Hatano-Nelson model. Our results generalize the celebrated ETH to the non-Hermitian setting, and they show how it affects the system dynamics, and how the salient signatures can be observed in present-day cold-atom experiments.
We present a theory to describe thermalization mechanism for time-periodic finite isolated interacting quantum systems. The long time asymptote of natural observables in Floquet states is directly related to averages of these observables governed by a time-independent effective Hamiltonian. We prove that if the effective system is nonintegrable and satisfies eigenstate thermalization hypothesis, quantum states of such time-periodic isolated systems will thermalize. After a long time evolution, system will relax to a stationary state, which only depends on an initial energy of the effective Hamiltonian and follows a generalized eigenstate thermalization hypothesis. A numerical test for the periodically modulated Bose-Hubbard model, with the extra nearest neighbor interaction on the bosonic lattice, agrees with the theoretical predictions.