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:2404.10224 · Physical review. E

Prethermalization in aperiodically driven classical spin systems

Sajag Kumar, Sayan Choudhury

Published Dec 26, 2024• 8 citations
arXivHTMLPDF

Abstract

Periodically driven classical many-body systems can host a rich zoo of prethermal dynamical phases. In this work, we extend the paradigm of classical prethermalization to aperiodically driven systems. We establish the existence of a long-lived prethermal regime in spin systems subjected to random multipolar drives. We demonstrate that the thermalization time scales as (1/T)^{2n+2}, where n is the multipolar order and T is the intrinsic time-scale associated with the drive. In the n→∞ limit, the drive becomes quasiperiodic and the thermalization time becomes exponentially long [∼exp(β/T)]. We further establish the robustness of prethermalization by demonstrating that these thermalization time scaling laws hold for a wide range of initial state energy densities. Intriguingly, the thermalization process in these classical systems is parametrically slower than their quantum counterparts, thereby highlighting important differences between classical and quantum prethermalization. Finally, we propose a protocol to harness this classical prethermalization to realize time rondeau crystals.

DOI
10.1103/physreve.110.064150

Related papers

Prethermalization in aperiodically kicked many-body dynamics

Jin Yan, Roderich Moessner, Hongzheng Zhao

Driven many-body systems typically experience heating due to the lack of energy conservation. Heating may be suppressed for time-periodic drives, but little is known for less regular drive protocols. In this paper, we investigate the heating dynamics in aperiodically kicked systems, specifically those driven by quasiperiodic Thue-Morse or a family of sequences with n -multipolar temporal correlations. We demonstrate that multiple heating channels can be eliminated . The number of eliminated channels increases with multipolar order n . We illustrate this in a classical kicked rotor chain where we find a long-lived prethermal regime. When the static Hamiltonian only involves the kinetic energy, the prethermal lifetime t* can strongly depend on the temporal correlations of the drive, with a power-law dependence on the t*∼K−2n , for which we can account using a simple linearization argument. Published by the American Physical Society 2024

arXiv:2306.16144•Physical review. B./Physical review. B•Feb 13, 2024•9 citations

Random Multipolar Driving: Tunably Slow Heating through Spectral Engineering

Hongzheng Zhao, Florian Mintert, Roderich Moessner +1 more

Driven quantum systems may realize novel phenomena absent in static systems, but driving-induced heating can limit the timescale on which these persist. We study heating in interacting quantum many-body systems driven by random sequences with n-multipolar correlations, corresponding to a polynomially suppressed low-frequency spectrum. For n≥1, we find a prethermal regime, the lifetime of which grows algebraically with the driving rate, with exponent 2n+1. A simple theory based on Fermi's golden rule accounts for this behavior. The quasiperiodic Thue-Morse sequence corresponds to the n→∞ limit and, accordingly, exhibits an exponentially long-lived prethermal regime. Despite the absence of periodicity in the drive, and in spite of its eventual heat death, the prethermal regime can host versatile nonequilibrium phases, which we illustrate with a random multipolar discrete time crystal.

arXiv:2007.07301•Physical Review Letters•Jan 28, 2021•63 citations

Anomalous random multipolar driven insulators

Hongzheng Zhao, Mark Spencer Rudner, Roderich Moessner +1 more

It is by now well established that periodically driven quantum many-body systems can realize topological nonequilibrium phases without any equilibrium counterpart. Here we show that, even in the absence of time translation symmetry, nonequilibrium topological phases of matter can exist in aperiodically driven systems for tunably parametrically long prethermal lifetimes. As a prerequisite, we first demonstrate the existence of long-lived prethermal Anderson localization in two dimensions under random multipolar driving. We then show that the localization may be topologically nontrivial with a quantized bulk orbital magnetization even though there are no well-defined Floquet operators. We further confirm the existence of this anomalous random multipolar driven insulator by detecting quantized charge pumping at the boundaries, which renders it experimentally observable.

arXiv:2201.05406•Physical review. B./Physical review. B•Jun 13, 2022•10 citations

Classical Prethermal Phases of Matter

Andrea Pizzi, Andreas Nunnenkamp, Johannes Knolle

Systems subject to a high-frequency drive can spend an exponentially long time in a prethermal regime, in which novel phases of matter with no equilibrium counterpart can be realized. Because of the notorious computational challenges of quantum many-body systems, numerical investigations in this direction have remained limited to one spatial dimension, in which long-range interactions have been proven a necessity. Here, we show that prethermal nonequilibrium phases of matter are not restricted to the quantum domain. Studying the Hamiltonian dynamics of a large three-dimensional lattice of classical spins, we provide the first numerical proof of prethermal phases of matter in a system with short-range interactions. Concretely, we find higher-order as well as fractional discrete time crystals breaking the time-translational symmetry of the drive with unexpectedly large integer as well as fractional periods. Our work paves the way toward the exploration of novel prethermal phenomena by means of classical Hamiltonian dynamics with virtually no limitations on the system's geometry or size, and thus with direct implications for experiments.

arXiv:2104.13928•Physical Review Letters•Sep 27, 2021•76 citations

Rigorous Bounds on the Heating Rate in Thue-Morse Quasiperiodically and Randomly Driven Quantum Many-Body Systems

Takashi Mori, Hongzheng Zhao, Florian Mintert +2 more

The nonequilibrium quantum dynamics of closed many-body systems is a rich yet challenging field. While recent progress for periodically driven (Floquet) systems has yielded a number of rigorous results, our understanding on quantum many-body systems driven by rapidly varying but aperiodic and quasiperiodic driving is still limited. Here, we derive rigorous, nonperturbative, bounds on the heating rate in quantum many-body systems under Thue-Morse quasiperiodic driving and under random multipolar driving, the latter being a tunably randomized variant of the former. In the process, we derive a static effective Hamiltonian that describes the transient prethermal state, including the dynamics of local observables. Our bound for Thue-Morse quasiperiodic driving suggests that the heating time scales like (ω/g)^{-C ln(ω/g)} with a positive constant C and a typical energy scale g of the Hamiltonian, in agreement with our numerical simulations.

arXiv:2101.07065•Physical Review Letters•Jul 30, 2021•35 citations

Floquet Phases of Matter via Classical Prethermalization

Bingtian Ye, Francisco Machado, Norman Y. Yao

We demonstrate that the prethermal regime of periodically driven (Floquet), classical many-body systems can host nonequilibrium phases of matter. In particular, we show that there exists an effective Hamiltonian that captures the dynamics of ensembles of classical trajectories despite the breakdown of this description at the single trajectory level. In addition, we prove that the effective Hamiltonian can host emergent symmetries protected by the discrete time-translation symmetry of the drive. The spontaneous breaking of such an emergent symmetry leads to a subharmonic response, characteristic of time crystalline order, that survives to exponentially late times in the frequency of the drive. To this end, we numerically demonstrate the existence of classical prethermal time crystals in systems with different dimensionalities and ranges of interaction. Extensions to higher order and fractional time crystals are also discussed.

arXiv:2104.13927•Physical Review Letters•Sep 27, 2021•57 citations
Periodically driven classical many-body systems can host a rich zoo of prethermal dynamical phases. In this work, we extend the paradigm of classical prethermalization to aperiodically driven systems. We establish the existence of a long-lived prethermal regime in spin systems subjected to random multipolar drives. We demonstrate that the thermalization time scales as (1/T)^{2n+2}, where n is the multipolar order and T is the intrinsic time-scale associated with the drive. In the n→∞ limit, the drive becomes quasiperiodic and the thermalization time becomes exponentially long [∼exp(β/T)]. We further establish the robustness of prethermalization by demonstrating that these thermalization time scaling laws hold for a wide range of initial state energy densities. Intriguingly, the thermalization process in these classical systems is parametrically slower than their quantum counterparts, thereby highlighting important differences between classical and quantum prethermalization. Finally, we propose a protocol to harness this classical prethermalization to realize time rondeau crystals.
Driven many-body systems typically experience heating due to the lack of energy conservation. Heating may be suppressed for time-periodic drives, but little is known for less regular drive protocols. In this paper, we investigate the heating dynamics in aperiodically kicked systems, specifically those driven by quasiperiodic Thue-Morse or a family of sequences with n -multipolar temporal correlations. We demonstrate that multiple heating channels can be eliminated . The number of eliminated channels increases with multipolar order n . We illustrate this in a classical kicked rotor chain where we find a long-lived prethermal regime. When the static Hamiltonian only involves the kinetic energy, the prethermal lifetime t* can strongly depend on the temporal correlations of the drive, with a power-law dependence on the t*∼K−2n , for which we can account using a simple linearization argument. Published by the American Physical Society 2024
Driven quantum systems may realize novel phenomena absent in static systems, but driving-induced heating can limit the timescale on which these persist. We study heating in interacting quantum many-body systems driven by random sequences with n-multipolar correlations, corresponding to a polynomially suppressed low-frequency spectrum. For n≥1, we find a prethermal regime, the lifetime of which grows algebraically with the driving rate, with exponent 2n+1. A simple theory based on Fermi's golden rule accounts for this behavior. The quasiperiodic Thue-Morse sequence corresponds to the n→∞ limit and, accordingly, exhibits an exponentially long-lived prethermal regime. Despite the absence of periodicity in the drive, and in spite of its eventual heat death, the prethermal regime can host versatile nonequilibrium phases, which we illustrate with a random multipolar discrete time crystal.
It is by now well established that periodically driven quantum many-body systems can realize topological nonequilibrium phases without any equilibrium counterpart. Here we show that, even in the absence of time translation symmetry, nonequilibrium topological phases of matter can exist in aperiodically driven systems for tunably parametrically long prethermal lifetimes. As a prerequisite, we first demonstrate the existence of long-lived prethermal Anderson localization in two dimensions under random multipolar driving. We then show that the localization may be topologically nontrivial with a quantized bulk orbital magnetization even though there are no well-defined Floquet operators. We further confirm the existence of this anomalous random multipolar driven insulator by detecting quantized charge pumping at the boundaries, which renders it experimentally observable.
Systems subject to a high-frequency drive can spend an exponentially long time in a prethermal regime, in which novel phases of matter with no equilibrium counterpart can be realized. Because of the notorious computational challenges of quantum many-body systems, numerical investigations in this direction have remained limited to one spatial dimension, in which long-range interactions have been proven a necessity. Here, we show that prethermal nonequilibrium phases of matter are not restricted to the quantum domain. Studying the Hamiltonian dynamics of a large three-dimensional lattice of classical spins, we provide the first numerical proof of prethermal phases of matter in a system with short-range interactions. Concretely, we find higher-order as well as fractional discrete time crystals breaking the time-translational symmetry of the drive with unexpectedly large integer as well as fractional periods. Our work paves the way toward the exploration of novel prethermal phenomena by means of classical Hamiltonian dynamics with virtually no limitations on the system's geometry or size, and thus with direct implications for experiments.
The nonequilibrium quantum dynamics of closed many-body systems is a rich yet challenging field. While recent progress for periodically driven (Floquet) systems has yielded a number of rigorous results, our understanding on quantum many-body systems driven by rapidly varying but aperiodic and quasiperiodic driving is still limited. Here, we derive rigorous, nonperturbative, bounds on the heating rate in quantum many-body systems under Thue-Morse quasiperiodic driving and under random multipolar driving, the latter being a tunably randomized variant of the former. In the process, we derive a static effective Hamiltonian that describes the transient prethermal state, including the dynamics of local observables. Our bound for Thue-Morse quasiperiodic driving suggests that the heating time scales like (ω/g)^{-C ln(ω/g)} with a positive constant C and a typical energy scale g of the Hamiltonian, in agreement with our numerical simulations.
We demonstrate that the prethermal regime of periodically driven (Floquet), classical many-body systems can host nonequilibrium phases of matter. In particular, we show that there exists an effective Hamiltonian that captures the dynamics of ensembles of classical trajectories despite the breakdown of this description at the single trajectory level. In addition, we prove that the effective Hamiltonian can host emergent symmetries protected by the discrete time-translation symmetry of the drive. The spontaneous breaking of such an emergent symmetry leads to a subharmonic response, characteristic of time crystalline order, that survives to exponentially late times in the frequency of the drive. To this end, we numerically demonstrate the existence of classical prethermal time crystals in systems with different dimensionalities and ranges of interaction. Extensions to higher order and fractional time crystals are also discussed.