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

New Journal of Physics

Exact Floquet flat band and heating suppression via two-tone drive protocols

Tista Banerjee, Sayan Choudhury, K. Sengupta

Published Aug 1, 2025• 6 citations
Publisher

Abstract

Abstract We demonstrate the existence of exact Floquet flat bands in a class of non-integrable quantum many-body Hamiltonians leading to strong violation of the eigenstate thermalization hypothesis in the presence of a two-tone drive characterized by frequencies Ω1 and Ω 2 = ν Ω 1 , where ν is an integer. We provide the exact analytic condition for this phenomenon to occur for a generic protocol. A small departure from the flat band conditions leads to suppression of heating over a long prethermal timescale in an otherwise ergodic many-body system away from integrable or perturbative regimes; we elucidate the central role of the flat band behind such heating suppression. Our analysis indicates the existence of a perturbative Floquet Hamiltonian, away from high drive frequency/amplitude limit, which controls the dynamics of the driven system near such flat bands. We demonstrate this phenomenon by exact numerical studies of Floquet bandwidth, spectral form factor, entanglement and Shannon entropies, heat absorption, and correlation functions of a driven Rydberg chain. We also study the corresponding micromotion which exhibits coherent reversal of excitations reminiscent of echoes; in addition, it harbors an exact reflection symmetry about t = T 1 / 2 , where T 1 = 2 π / Ω 1 , which we elucidate. We discuss experiments which can test our theory.

DOI
10.1088/1367-2630/adfd07

Related papers

Exact Floquet flat band and heating suppression via two-rate drive protocols

Banerjee, Tista, Sayan Choudhury, K. Sengupta

We demonstrate the existence of exact Floquet flat bands implying strong violation of the eigenstate thermalization hypothesis in a large class of closed quantum many-body systems in the presence of a two-rate drive characterized by frequencies $Ω_1$ and $Ω_2=νΩ_1$. We provide the exact analytic condition for this phenomenon to occur for a generic protocol; in particular, $ν=(2p+1)$, where $p$ is an integer, leads to such flat bands for both square-pulse and cosine drive protocols for arbitrary $Ω_1$. In the vicinity of these points, heating is suppressed up to very long timescales in such driven systems, leading to a prethermal regime; we demonstrate this by exact numerical studies of distribution and bandwidth of the Floquet eigenstates, spectral form factor, entanglement entropy, and correlation functions of an experimentally realizable finite driven Rydberg chain. The corresponding micromotion exhibits coherent reversal of excitations reminiscent of echoes. Our analysis constitutes a yet unexplored mechanism for heating suppression in driven closed quantum systems.

arXiv:2404.06536•Apr 9, 2024•0 citations

Emergent conservation in the Floquet dynamics of integrable non-Hermitian models

Tista Banerjee, K. Sengupta

We study the dynamics of a class of integrable non-Hermitian free-fermionic models driven periodically using a continuous drive protocol characterized by an amplitude ${g}_{1}$ and frequency ${\ensuremath{\omega}}_{D}$. We derive an analytic, albeit perturbative, Floquet Hamiltonian for describing such systems using Floquet perturbation theory with ${g}_{1}^{\ensuremath{-}1}$ being the perturbation parameter. Our analysis indicates the existence of special drive frequencies at which an approximately conserved quantity emerges. The presence of such an almost conserved quantity is reflected in the dynamics of the fidelity, the correlation functions, and the half-chain entanglement entropy of the driven system. In addition, it also controls the nature of the steady state of the system. We show that one-dimensional transverse field Ising model, with an imaginary component of the transverse field, serves as an experimentally relevant example of this phenomenon. In this case, the transverse magnetization is approximately conserved; this conservation leads to complete suppression of oscillatory features in the transient dynamics of fidelity, magnetization, and entanglement of the driven chain at special drive frequencies. We discuss the nature of the steady state of the Ising chain near and away from these special frequencies, demonstrate the protocol independence of this phenomenon by showing its existence for discrete drive protocols, and suggest experiments which can test our theory.

arXiv:2209.12939•Physical review. B./Physical review. B•Apr 10, 2023•16 citations

Resonant pair production and flat band melting in a driven Rydberg chain

Tista Banerjee, K. Sengupta

We study a Rydberg chain subjected to a two-tone periodic drive of the detuning $Δ(t)$ and Rabi frequency $Ω(t)$ at frequencies $ω_1$ and $ω_2=νω_1$ respectively with $ν\in \mathbf{Z}$. In the strong Rydberg blockade limit, such a system reduces to the PXP model and exhibits exact Floquet flat band. Here we determine, using a time-dependent Schrieffer-Wolff transformation, the domain of validity of such PXP dynamics once the blockade-violating processes are taken into account. We study the melting of such flat bands in the presence of strong, but finite, blockade strength. Using Floquet perturbation theory (FPT), we identify two mechanisms for such melting; the first occurs due to the presence of many-body resonances involving resonant production of nearest-neighbor Rydberg excitation pairs while the second involves virtual processes that access intermediate states with such pairs. Our analytical FPT results match with those obtained using exact diagonalization on a finite chain. We study the dynamics for $|{\rm vac}\rangle$ (Fock state with no Rydberg excitation), $|{\mathbb {Z}}_2\rangle$, and $|{\mathbb {Z}}_3\rangle$ (Fock states with Rydberg excitations on alternate and every third site respectively) initial states. We find that $|{\rm vac}\rangle$ shows exceptional stability against resonant pair formation while $|{\mathbb {Z}}_3\rangle$ exhibits flat band melting via virtual processes away from the direct resonances. We find oscillatory dynamics with large time period for the $|{\mathbb {Z}}_2\rangle$ initial state and the presence of Floquet scars that have large overlap with $|{\mathbb {Z}}_3\rangle$ state; these phenomena occur due to processes that are absent in the PXP limit. We propose measurement of nearest neighbor pair correlation functions using Rydberg atom quantum simulator platforms as an accessible experimental probe for these effects.

quant-pharXiv:2610.22532•Oct 19, 2026•0 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

Mapping as a probe for heating suppression in periodically driven quantum many-body systems

Étienne Wamba, Axel Pelster, J. R. Anglin

Experiments on periodically driven quantum systems have effectively realized quasi-Hamiltonians, in the sense of Floquet theory, that are otherwise inaccessible in static condensed matter systems. Although the Floquet quasi-Hamiltonians are time-independent, however, these continuously driven systems can still suffer from heating due to a secular growth in the expectation value of the time-dependent physical Hamiltonian. Here we use an exact space-time mapping to construct a class of many-body systems with rapid periodic driving which we nonetheless prove to be completely free of heating, by mapping them exactly onto time-independent systems. The absence of heating despite the periodic driving occurs in these cases of harmonically trapped dilute Bose gas because the driving is a certain periodic but anharmonic modulation of the gas's two-body contact interaction, at a particular frequency. Although we prove that the absence of heating is exact within full quantum many-body theory, we then use mean-field theory to simulate 'Floquet heating spectroscopy' and compute the heating rate when the driving frequency is varied away from the critical value for zero heating. In both weakly and strongly non-linear regimes, the heating rate as a function of driving frequency appears to show a number of Fano resonances, suggesting that the exactly proven absence of heating at the critical frequency may be explained in terms of destructive interferences between excitation modes.

arXiv:2108.07171•Aug 16, 2021•0 citations

Emergent prethermal Bethe integrability in a periodically driven Rydberg chain

Saptadip Roy, Arnab Sen, Diptiman Sen +1 more

We study a chain of periodically driven Rydberg atoms and identify a class of drive protocols for which the system exhibits emergent prethermal Bethe integrability at special drive frequencies. We provide a perturbative analytic expression of its Floquet Hamiltonian in the large drive amplitude regime. We demonstrate integrability of the leading term of this Floquet Hamiltonian at special drive frequencies, which we identify, by mapping it to the Hamiltonian of the paradigmatic spin-$1/2$ ${\rm XXZ}$ chain. We support our analytical results by exact diagonalization studies on finite chains. Our numerical results on level statistics, half-chain entanglement entropy, and longitudinal magnetization of the driven chain brings out its emergent integrable nature at the special drive frequencies which persists up to a large prethermal timescale.

quant-pharXiv:2604.24850•Apr 29, 2026•0 citations
Abstract We demonstrate the existence of exact Floquet flat bands in a class of non-integrable quantum many-body Hamiltonians leading to strong violation of the eigenstate thermalization hypothesis in the presence of a two-tone drive characterized by frequencies Ω1 and Ω 2 = ν Ω 1 , where ν is an integer. We provide the exact analytic condition for this phenomenon to occur for a generic protocol. A small departure from the flat band conditions leads to suppression of heating over a long prethermal timescale in an otherwise ergodic many-body system away from integrable or perturbative regimes; we elucidate the central role of the flat band behind such heating suppression. Our analysis indicates the existence of a perturbative Floquet Hamiltonian, away from high drive frequency/amplitude limit, which controls the dynamics of the driven system near such flat bands. We demonstrate this phenomenon by exact numerical studies of Floquet bandwidth, spectral form factor, entanglement and Shannon entropies, heat absorption, and correlation functions of a driven Rydberg chain. We also study the corresponding micromotion which exhibits coherent reversal of excitations reminiscent of echoes; in addition, it harbors an exact reflection symmetry about t = T 1 / 2 , where T 1 = 2 π / Ω 1 , which we elucidate. We discuss experiments which can test our theory.
We demonstrate the existence of exact Floquet flat bands implying strong violation of the eigenstate thermalization hypothesis in a large class of closed quantum many-body systems in the presence of a two-rate drive characterized by frequencies Ω1Ω_1Ω1​ and Ω2=νΩ1Ω_2=νΩ_1Ω2​=νΩ1​. We provide the exact analytic condition for this phenomenon to occur for a generic protocol; in particular, ν=(2p+1)ν=(2p+1)ν=(2p+1), where ppp is an integer, leads to such flat bands for both square-pulse and cosine drive protocols for arbitrary Ω1Ω_1Ω1​. In the vicinity of these points, heating is suppressed up to very long timescales in such driven systems, leading to a prethermal regime; we demonstrate this by exact numerical studies of distribution and bandwidth of the Floquet eigenstates, spectral form factor, entanglement entropy, and correlation functions of an experimentally realizable finite driven Rydberg chain. The corresponding micromotion exhibits coherent reversal of excitations reminiscent of echoes. Our analysis constitutes a yet unexplored mechanism for heating suppression in driven closed quantum systems.
We study the dynamics of a class of integrable non-Hermitian free-fermionic models driven periodically using a continuous drive protocol characterized by an amplitude g1{g}_{1}g1​ and frequency ${\ensuremath{\omega}}_{D}$. We derive an analytic, albeit perturbative, Floquet Hamiltonian for describing such systems using Floquet perturbation theory with ${g}_{1}^{\ensuremath{-}1}$ being the perturbation parameter. Our analysis indicates the existence of special drive frequencies at which an approximately conserved quantity emerges. The presence of such an almost conserved quantity is reflected in the dynamics of the fidelity, the correlation functions, and the half-chain entanglement entropy of the driven system. In addition, it also controls the nature of the steady state of the system. We show that one-dimensional transverse field Ising model, with an imaginary component of the transverse field, serves as an experimentally relevant example of this phenomenon. In this case, the transverse magnetization is approximately conserved; this conservation leads to complete suppression of oscillatory features in the transient dynamics of fidelity, magnetization, and entanglement of the driven chain at special drive frequencies. We discuss the nature of the steady state of the Ising chain near and away from these special frequencies, demonstrate the protocol independence of this phenomenon by showing its existence for discrete drive protocols, and suggest experiments which can test our theory.
We study a Rydberg chain subjected to a two-tone periodic drive of the detuning Δ(t)Δ(t)Δ(t) and Rabi frequency Ω(t)Ω(t)Ω(t) at frequencies ω1ω_1ω1​ and ω2=νω1ω_2=νω_1ω2​=νω1​ respectively with ν∈Zν\in \mathbf{Z}ν∈Z. In the strong Rydberg blockade limit, such a system reduces to the PXP model and exhibits exact Floquet flat band. Here we determine, using a time-dependent Schrieffer-Wolff transformation, the domain of validity of such PXP dynamics once the blockade-violating processes are taken into account. We study the melting of such flat bands in the presence of strong, but finite, blockade strength. Using Floquet perturbation theory (FPT), we identify two mechanisms for such melting; the first occurs due to the presence of many-body resonances involving resonant production of nearest-neighbor Rydberg excitation pairs while the second involves virtual processes that access intermediate states with such pairs. Our analytical FPT results match with those obtained using exact diagonalization on a finite chain. We study the dynamics for ∣vac⟩|{\rm vac}\rangle∣vac⟩ (Fock state with no Rydberg excitation), ∣Z2⟩|{\mathbb {Z}}_2\rangle∣Z2​⟩, and ∣Z3⟩|{\mathbb {Z}}_3\rangle∣Z3​⟩ (Fock states with Rydberg excitations on alternate and every third site respectively) initial states. We find that ∣vac⟩|{\rm vac}\rangle∣vac⟩ shows exceptional stability against resonant pair formation while ∣Z3⟩|{\mathbb {Z}}_3\rangle∣Z3​⟩ exhibits flat band melting via virtual processes away from the direct resonances. We find oscillatory dynamics with large time period for the ∣Z2⟩|{\mathbb {Z}}_2\rangle∣Z2​⟩ initial state and the presence of Floquet scars that have large overlap with ∣Z3⟩|{\mathbb {Z}}_3\rangle∣Z3​⟩ state; these phenomena occur due to processes that are absent in the PXP limit. We propose measurement of nearest neighbor pair correlation functions using Rydberg atom quantum simulator platforms as an accessible experimental probe for these effects.
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.
Experiments on periodically driven quantum systems have effectively realized quasi-Hamiltonians, in the sense of Floquet theory, that are otherwise inaccessible in static condensed matter systems. Although the Floquet quasi-Hamiltonians are time-independent, however, these continuously driven systems can still suffer from heating due to a secular growth in the expectation value of the time-dependent physical Hamiltonian. Here we use an exact space-time mapping to construct a class of many-body systems with rapid periodic driving which we nonetheless prove to be completely free of heating, by mapping them exactly onto time-independent systems. The absence of heating despite the periodic driving occurs in these cases of harmonically trapped dilute Bose gas because the driving is a certain periodic but anharmonic modulation of the gas's two-body contact interaction, at a particular frequency. Although we prove that the absence of heating is exact within full quantum many-body theory, we then use mean-field theory to simulate 'Floquet heating spectroscopy' and compute the heating rate when the driving frequency is varied away from the critical value for zero heating. In both weakly and strongly non-linear regimes, the heating rate as a function of driving frequency appears to show a number of Fano resonances, suggesting that the exactly proven absence of heating at the critical frequency may be explained in terms of destructive interferences between excitation modes.
We study a chain of periodically driven Rydberg atoms and identify a class of drive protocols for which the system exhibits emergent prethermal Bethe integrability at special drive frequencies. We provide a perturbative analytic expression of its Floquet Hamiltonian in the large drive amplitude regime. We demonstrate integrability of the leading term of this Floquet Hamiltonian at special drive frequencies, which we identify, by mapping it to the Hamiltonian of the paradigmatic spin-1/21/21/2 XXZ{\rm XXZ}XXZ chain. We support our analytical results by exact diagonalization studies on finite chains. Our numerical results on level statistics, half-chain entanglement entropy, and longitudinal magnetization of the driven chain brings out its emergent integrable nature at the special drive frequencies which persists up to a large prethermal timescale.