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:2412.10498 · Physical Review X

Floquet Thermalization via Instantons near Dynamical Freezing

Rohit Mukherjee, Haoyu Guo, Debanjan Chowdhury

Published Jan 28, 2026• 6 citations
arXivHTMLPDF

Abstract

Periodically driven Floquet quantum many-body systems have revealed new insights into the rich interplay of thermalization and growth of entanglement. The phenomenology of , whereby a translationally invariant many-body system exhibits emergent conservation laws and a slow growth of entanglement entropy at certain fixed ratios of a drive amplitude and frequency, presents a novel paradigm for retaining memory of an initial state up to late times. Previous studies of dynamical freezing have largely been restricted to a high-frequency Floquet-Magnus expansion and numerical exact diagonalization. Both techniques are unable to capture the slow approach to thermalization, or lack thereof, in a systematic fashion. By employing Floquet , where the time-dependent part of the Hamiltonian is gradually decoupled from the effective Hamiltonian using a sequence of unitary transformations, we unveil the universal approach to dynamical freezing and beyond, at asymptotically late times. We analyze the behavior associated with the flow renormalization at and near freezing using both exact-diagonalization and tensor-network-based methods and contrast the results with the conventional prethermal phenomenon. For a generic nonintegrable spin Hamiltonian with a periodic cosine wave drive, the flow approaches an unstable fixed point with an approximate emergent symmetry. We observe that at freezing the thermalization timescales are delayed compared to away from freezing, and the flow trajectory undergoes a series of events. Our numerical results are supported by analytical solutions to the flow equations.

DOI
10.1103/4w5w-57my

Related papers

Dynamical Freezing in Exactly Solvable Models of Driven Chaotic Quantum Dots

Haoyu Guo, Rohit Mukherjee, Debanjan Chowdhury

The late-time equilibrium behavior of generic interacting models is determined by the coupled hydrodynamic equations associated with the globally conserved quantities. In the presence of an external time-dependent drive, nonintegrable systems typically thermalize to an effectively infinite-temperature state, losing all memory of their initial states. However, in the presence of a large time-periodic Floquet drive, there exist special points in phase space where the strongly interacting system develops approximate emergent conservation laws. Here, we present results for an exactly solvable model of two coupled chaotic quantum dots with multiple orbitals interacting via random two- and four-fermion interactions in the presence of a Floquet drive. We analyze the phenomenology of dynamically generated freezing using a combination of exact diagonalization and field-theoretic analysis in the limit of a large number of electronic orbitals. The model displays universal freezing behavior irrespective of whether the theory is averaged over the disorder configurations or not. We present explicit computations for the growth of many-body chaos and entanglement entropy, which demonstrates the long-lived coherence associated with the interacting degrees of freedom even at late times at the dynamically frozen points. We also compute the slow timescale that controls relaxation away from exact freezing in a high-frequency expansion.

arXiv:2405.01627•Physical Review Letters•May 12, 2025•13 citations

Arresting quantum chaos dynamically in transmon arrays

Rohit Mukherjee, Haoyu Guo, Keiran Lewellen +1 more

Ergodic quantum many-body systems evolving under unitary time dynamics typically lose memory of their initial state via information scrambling. Here, we consider a paradigmatic translationally invariant many-body Hamiltonian of interacting bosons—a Josephson junction array in the transmon regime—in the presence of a strong Floquet drive. Generically, such a time-dependent drive is expected to heat the system to an effectively infinite-temperature, featureless state in the late-time limit. However, using numerical exact diagonalization, we find evidence of special ratios of the drive amplitude and frequency where the system develops emergent conservation laws and approximate integrability. Remarkably, at these same set of points, the Lyapunov exponent associated with the semi-classical dynamics for the coupled many-body equations of motion drops by at least an order of magnitude, arresting the growth of chaos. We supplement our numerical results with an analytical Floquet-Magnus expansion that includes higher-order corrections and capture the slow dynamics that control decay away from exact freezing.

arXiv:2405.14935•Newton•Feb 6, 2025•5 citations

High-Frequency Floquet Renormalization of Many-Body Dynamics: Suppression of Thermalization in a Prethermal Regime

Claudia Attaianese

This work presents a theoretical investigation of dynamic stabilization in interacting quantum many-body systems via high-frequency periodic driving. Using Floquet theory and the Magnus expansion, we derive the effective time-independent Hamiltonian governing the slow dynamics of a driven spin chain. We show that the external field induces a parametric renormalization of the transverse tunneling terms through a zeroth-order Bessel function dependence, leading to a critical drive amplitude at which transport is strongly suppressed. This suppression of the lowest-order hopping term gives rise to a long-lived prethermal regime in which many-body thermalization is significantly delayed. The resulting dynamics exhibit a sharp reduction in the short-to-intermediate time entanglement entropy growth rate. The framework is consistent with known results in Floquet engineering and coherent destruction of tunneling, and provides a unified interpretation of transport suppression and delayed scrambling in periodically driven systems. A falsifiable experimental protocol using ultracold atoms in optical lattices is proposed to validate the predicted threshold behavior and prethermal stabilization mechanism.

•Mar 23, 2026•0 citations

Emergent strong zero mode through local Floquet engineering

Bhaskar Mukherjee, Ronald Melendrez, Marcin Szyniszewski +2 more

Periodically driven quantum systems host exotic phenomena that often do not have any analog in undriven systems. Floquet prethermalization and dynamical freezing of certain observables, via the emergence of conservation laws, are realized by controlling the drive frequency. Recent experimental developments in synthetic quantum matter, such as superconducting qubits and cold atoms, have opened avenues for implementing local Floquet engineering which can achieve spatially modulated quantum control of states. Here, we uncover the novel memory effects of local periodic driving in a nonintegrable spin-half staggered Heisenberg chain. For a boundary-driven protocol at the dynamical freezing frequency, we show the formation of an approximate strong zero mode, a prethermal quasilocal operator, due to the emergence of a discrete global Z2 symmetry. This is captured by constructing an accurate effective Floquet Hamiltonian using a higher-order partially resummed Floquet-Magnus expansion. The lifetime of the boundary spin can be exponentially enhanced by enlarging the set of suitably chosen driven sites. We demonstrate that in the asymptotic limit, achieved by increasing the number of driven sites, a strong zero mode emerges, where the lifetime of the boundary spin grows exponentially with system size. The nonlocal processes in the Floquet Hamiltonian play a pivotal role in the total freezing of the boundary spin in the thermodynamic limit. The novel dynamics of the boundary spin is accompanied by a rich structure of entanglement in the Floquet eigenstates where specific bipartitions yield an area-law scaling while the entanglement for random bipartitions scales as a volume-law. Our work addresses the long-standing question of the existence of a strong zero mode in a nonintegrable model and elucidates the complex nature of thermalization in locally driven systems. Published by the American Physical Society 2024

arXiv:2306.01835•Physical review. B./Physical review. B•Feb 8, 2024•14 citations

Floquet (Pre-)thermalization in Many-Body Systems away from the High-Frequency Limit

Christoph Fleckenstein, Marin Bukov

We investigate a class of periodically driven many-body systems that allows us to extend the phenomenon of prethermalization to the vicinity of isolated intermediate-to-low drive frequencies away from the high-frequency limit. We provide numerical evidence for the formation of a parametrically long-lived prethermal plateau, captured by an effective Floquet Hamiltonian computed using the replica inverse-frequency expansion, and demonstrate its stability w.r.t.~random perturbations in the drive period. Considering exclusively nonintegrable Floquet Hamiltonians, we find that heating rates are non-universal: we observe Fermi's Golden Rule scaling, power-law scaling inconsistent with the Golden Rule, and non-power law scaling, depending on the drive. Despite the asymptotic character of the inverse-frequency expansion, we show that it describes the thermostatic properties of the state all along the evolution up to infinite temperature, with higher-order terms improving the accuracy. Our results suggest a dynamical mechanism to gradually increase temperature in isolated quantum simulators, such as ultracold atoms, and open up an alternative possibility to investigate thermal phase transitions and the interplay between thermal and quantum criticality using Floquet drives.

•Dec 21, 2020•0 citations

Flow Renormalization and Emergent Prethermal Regimes of Periodically-Driven Quantum Systems

Martin Claassen

We develop a flow renormalization approach for periodically-driven quantum systems, which reveals prethermal dynamical regimes and associated timescales via direct correspondence between real time and flow time behavior. In this formalism, the dynamical problem is recast in terms of coupling constants of the theory flowing towards an attractive fixed point that represents the thermal Floquet Hamiltonian at long times, while narrowly avoiding a series of unstable fixed points which determine distinct prethermal regimes at intermediate times. We study a class of relevant perturbations that trigger the onset of heating and thermalization, and demonstrate that the renormalization flow has an elegant representation in terms of a flow of matrix product operators. Our results permit microscopic calculations of the emergence of distinct dynamical regimes directly in the thermodynamic limit in an efficient manner, establishing a new computational tool for driven non-equilibrium systems.

arXiv:2103.07485•Mar 12, 2021•2 citations
Periodically driven Floquet quantum many-body systems have revealed new insights into the rich interplay of thermalization and growth of entanglement. The phenomenology of , whereby a translationally invariant many-body system exhibits emergent conservation laws and a slow growth of entanglement entropy at certain fixed ratios of a drive amplitude and frequency, presents a novel paradigm for retaining memory of an initial state up to late times. Previous studies of dynamical freezing have largely been restricted to a high-frequency Floquet-Magnus expansion and numerical exact diagonalization. Both techniques are unable to capture the slow approach to thermalization, or lack thereof, in a systematic fashion. By employing Floquet , where the time-dependent part of the Hamiltonian is gradually decoupled from the effective Hamiltonian using a sequence of unitary transformations, we unveil the universal approach to dynamical freezing and beyond, at asymptotically late times. We analyze the behavior associated with the flow renormalization at and near freezing using both exact-diagonalization and tensor-network-based methods and contrast the results with the conventional prethermal phenomenon. For a generic nonintegrable spin Hamiltonian with a periodic cosine wave drive, the flow approaches an unstable fixed point with an approximate emergent symmetry. We observe that at freezing the thermalization timescales are delayed compared to away from freezing, and the flow trajectory undergoes a series of events. Our numerical results are supported by analytical solutions to the flow equations.
The late-time equilibrium behavior of generic interacting models is determined by the coupled hydrodynamic equations associated with the globally conserved quantities. In the presence of an external time-dependent drive, nonintegrable systems typically thermalize to an effectively infinite-temperature state, losing all memory of their initial states. However, in the presence of a large time-periodic Floquet drive, there exist special points in phase space where the strongly interacting system develops approximate emergent conservation laws. Here, we present results for an exactly solvable model of two coupled chaotic quantum dots with multiple orbitals interacting via random two- and four-fermion interactions in the presence of a Floquet drive. We analyze the phenomenology of dynamically generated freezing using a combination of exact diagonalization and field-theoretic analysis in the limit of a large number of electronic orbitals. The model displays universal freezing behavior irrespective of whether the theory is averaged over the disorder configurations or not. We present explicit computations for the growth of many-body chaos and entanglement entropy, which demonstrates the long-lived coherence associated with the interacting degrees of freedom even at late times at the dynamically frozen points. We also compute the slow timescale that controls relaxation away from exact freezing in a high-frequency expansion.
Ergodic quantum many-body systems evolving under unitary time dynamics typically lose memory of their initial state via information scrambling. Here, we consider a paradigmatic translationally invariant many-body Hamiltonian of interacting bosons—a Josephson junction array in the transmon regime—in the presence of a strong Floquet drive. Generically, such a time-dependent drive is expected to heat the system to an effectively infinite-temperature, featureless state in the late-time limit. However, using numerical exact diagonalization, we find evidence of special ratios of the drive amplitude and frequency where the system develops emergent conservation laws and approximate integrability. Remarkably, at these same set of points, the Lyapunov exponent associated with the semi-classical dynamics for the coupled many-body equations of motion drops by at least an order of magnitude, arresting the growth of chaos. We supplement our numerical results with an analytical Floquet-Magnus expansion that includes higher-order corrections and capture the slow dynamics that control decay away from exact freezing.
This work presents a theoretical investigation of dynamic stabilization in interacting quantum many-body systems via high-frequency periodic driving. Using Floquet theory and the Magnus expansion, we derive the effective time-independent Hamiltonian governing the slow dynamics of a driven spin chain. We show that the external field induces a parametric renormalization of the transverse tunneling terms through a zeroth-order Bessel function dependence, leading to a critical drive amplitude at which transport is strongly suppressed. This suppression of the lowest-order hopping term gives rise to a long-lived prethermal regime in which many-body thermalization is significantly delayed. The resulting dynamics exhibit a sharp reduction in the short-to-intermediate time entanglement entropy growth rate. The framework is consistent with known results in Floquet engineering and coherent destruction of tunneling, and provides a unified interpretation of transport suppression and delayed scrambling in periodically driven systems. A falsifiable experimental protocol using ultracold atoms in optical lattices is proposed to validate the predicted threshold behavior and prethermal stabilization mechanism.
Periodically driven quantum systems host exotic phenomena that often do not have any analog in undriven systems. Floquet prethermalization and dynamical freezing of certain observables, via the emergence of conservation laws, are realized by controlling the drive frequency. Recent experimental developments in synthetic quantum matter, such as superconducting qubits and cold atoms, have opened avenues for implementing local Floquet engineering which can achieve spatially modulated quantum control of states. Here, we uncover the novel memory effects of local periodic driving in a nonintegrable spin-half staggered Heisenberg chain. For a boundary-driven protocol at the dynamical freezing frequency, we show the formation of an approximate strong zero mode, a prethermal quasilocal operator, due to the emergence of a discrete global Z2 symmetry. This is captured by constructing an accurate effective Floquet Hamiltonian using a higher-order partially resummed Floquet-Magnus expansion. The lifetime of the boundary spin can be exponentially enhanced by enlarging the set of suitably chosen driven sites. We demonstrate that in the asymptotic limit, achieved by increasing the number of driven sites, a strong zero mode emerges, where the lifetime of the boundary spin grows exponentially with system size. The nonlocal processes in the Floquet Hamiltonian play a pivotal role in the total freezing of the boundary spin in the thermodynamic limit. The novel dynamics of the boundary spin is accompanied by a rich structure of entanglement in the Floquet eigenstates where specific bipartitions yield an area-law scaling while the entanglement for random bipartitions scales as a volume-law. Our work addresses the long-standing question of the existence of a strong zero mode in a nonintegrable model and elucidates the complex nature of thermalization in locally driven systems. Published by the American Physical Society 2024
We investigate a class of periodically driven many-body systems that allows us to extend the phenomenon of prethermalization to the vicinity of isolated intermediate-to-low drive frequencies away from the high-frequency limit. We provide numerical evidence for the formation of a parametrically long-lived prethermal plateau, captured by an effective Floquet Hamiltonian computed using the replica inverse-frequency expansion, and demonstrate its stability w.r.t.~random perturbations in the drive period. Considering exclusively nonintegrable Floquet Hamiltonians, we find that heating rates are non-universal: we observe Fermi's Golden Rule scaling, power-law scaling inconsistent with the Golden Rule, and non-power law scaling, depending on the drive. Despite the asymptotic character of the inverse-frequency expansion, we show that it describes the thermostatic properties of the state all along the evolution up to infinite temperature, with higher-order terms improving the accuracy. Our results suggest a dynamical mechanism to gradually increase temperature in isolated quantum simulators, such as ultracold atoms, and open up an alternative possibility to investigate thermal phase transitions and the interplay between thermal and quantum criticality using Floquet drives.
We develop a flow renormalization approach for periodically-driven quantum systems, which reveals prethermal dynamical regimes and associated timescales via direct correspondence between real time and flow time behavior. In this formalism, the dynamical problem is recast in terms of coupling constants of the theory flowing towards an attractive fixed point that represents the thermal Floquet Hamiltonian at long times, while narrowly avoiding a series of unstable fixed points which determine distinct prethermal regimes at intermediate times. We study a class of relevant perturbations that trigger the onset of heating and thermalization, and demonstrate that the renormalization flow has an elegant representation in terms of a flow of matrix product operators. Our results permit microscopic calculations of the emergence of distinct dynamical regimes directly in the thermodynamic limit in an efficient manner, establishing a new computational tool for driven non-equilibrium systems.