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:2603.23493

Tunable Floquet selection rules in a driven Ising chain

Rishi Paresh Joshi, Sanchayan Banerjee, Sneha Narasimha Moorthy, Tapan Mishra

Published Mar 24, 2026• 0 citations
arXivHTMLPDF

Abstract

We study a periodically driven spin-$1/2$ Ising chain with a nearest-neighbour coupling and longitudinal field while a weak transverse field induces single-spin flips. Through Floquet perturbation theory (FPT), we obtain signatures of Hilbert space fragmentation (HSF) and an unconventional form of dynamical localisation which we call the Floquet freezing. Our analysis suggests that these observations emerge due to a single Floquet selection rule that dictates the prethermal dynamics. For a special value of the field-to-interaction strength ratio together with commensurate drive periods, this rule permits only a constrained subset of bulk spin flips, leading to prethermal HSF in the full spin-$1/2$ Hilbert space. Under open boundary conditions, the same rule suppresses boundary spin flips up to higher order in perturbation and produces long-lived prethermal edge memory, which is neither topological in origin nor is a strong zero mode. Furthermore, under periodic boundary conditions, the largest surviving fragment is exactly the PXP sector at leading order and therefore exhibits Floquet-inherited scar phenomenology in the prethermal window. At higher commensurate ratios of field strength to interaction strength, all first-order single-spin-flip channels are suppressed and the system enters a regime of Floquet freezing. Hence, our study leverages the selection rules obtained through Floquet perturbation theory to obtain exotic prethermal phenomena at different parameter regimes.

DOI
10.48550/arxiv.2603.23493

Related papers

Floquet scars and prethermal fragmentation in a driven spin-one chain

Krishanu Ghosh, Diptiman Sen, K. Sengupta

We study the periodic dynamics of a spin-one chain driven using a square-pulse protocol with amplitude $Q_0$ and frequency $ω_D$. The Hamiltonian of the spin chain hosts a thermodynamically large number of $Z_2$-valued conserved quantities $W_{\ell}$ on the links $\ell$. This allows us to study the Floquet dynamics of this chain within a given sector with fixed values of $W_{\ell}$. For the sector with all $W_{\ell}=1$, we find signatures of quantum many-body scar states for $\hbar ω_D \gg Q_0$; they lead to oscillatory dynamics and fidelity revival for specific initial states. Upon lowering $ω_D$, we find an ergodic regime exhibiting fast thermalization consistent with the prediction of the (Floquet) eigenstate thermalization hypothesis. In addition, we identify special drive frequencies $ω_n^{\ast}= Q_0/(2n \hbar)$ (where $n = 1, 2, 3, \cdots$) at which the Floquet Hamiltonian exhibits prethermal strong Hilbert space fragmentation (HSF) with the largest fragment being ergodic; in contrast, a weak HSF is found at $ω'_n= Q_0/[\hbar(2n+1)]$ (where $n = 0, 1, 2, \cdots$). We also study the sector with $W_{\ell} =\{\cdots 1,1,-1,1,1,-1 \cdots \}$ which shows strong HSF at $ω_n^{\ast}$ but no fragmentation at $ω'_n$. Our analysis indicates that the strong HSF in this sector harbors an integrable largest fragment. We provide numerical support for our analytical and perturbative results using exact-diagonalization (ED) studies on finite chains of length $L\le 24$. Our numerical results for entanglement entropy, fidelity, and correlation functions of the driven chain provide definitive signatures of prethermal strong HSF for both sectors.

cond-mat.stat-mechCross-listedarXiv:2603.06111•Mar 9, 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 engineering of Hilbert space fragmentation in Stark lattices

L Zhang, Yongguan Ke, Ling Lin +1 more

The concept of Hilbert space fragmentation (HSF) has recently been put forward as a routine to break quantum ergodicity. Although HSF exists widely in models with dynamical constraints, it is still challenging to tune it. Here, we propose a scheme to tune the HSF in a one-dimensional tilted lattice of interacting spinless fermions with periodically driven tunneling. For weak tunneling strength, the dynamics for a long range of time is governed by effective Hamiltonians with kinetic constraints, which appear as density-dependent tunneling. Through a Floquet time-dependent perturbation theory, we analytically derive two different resonance frequencies, at which some particular tunneling processes are resonant. At the nonresonance frequencies, the system is strongly constrained and exhibits a strong HSF. At the two different resonance frequencies, the kinetic constraints are partly released and the system exhibits another two different strong HSFs. We can tune the HSF by changing the driving frequency. We support the perturbation analysis with exact numerical simulation of the entanglement entropy, the density correlation functions, and the saturated local density profiles. Our result provides a promising way to control HSF through Floquet engineering.

arXiv:2311.11771•Physical review. B./Physical review. B•May 29, 2024•8 citations

Prethermal Fragmentation in a Periodically Driven Fermionic Chain

Somsubhra Ghosh, Indranil Paul, K. Sengupta

We study a fermionic chain with nearest-neighbor hopping and density-density interactions, where the nearest-neighbor interaction term is driven periodically. We show that such a driven chain exhibits prethermal strong Hilbert space fragmentation (HSF) in the high drive amplitude regime at specific drive frequencies ω_{m}^{*}. This constitutes the first realization of HSF for out-of-equilibrium systems. We obtain analytic expressions of ω_{m}^{*} using a Floquet perturbation theory and provide exact numerical computation of entanglement entropy, equal-time correlation functions, and the density autocorrelation of fermions for finite chains. All of these quantities indicate clear signatures of strong HSF. We study the fate of the HSF as one tunes away from ω_{m}^{*} and discuss the extent of the prethermal regime as a function of the drive amplitude.

arXiv:2212.03892•Physical Review Letters•Mar 23, 2023•23 citations

Effective and Floquet Hamiltonians for High Frequency Driving and Floquet-induced Heating in Quantum Spin Chains

Mayukh Bandyopadhyay, Vinod Ashokan

We study the non-equilibrium dynamics of a disordered periodically driven quantum spin chain, with the competition between the interaction, disorder, and Floquet driving being of particular interest. We study dynamics of entanglement entropy, energy absorption to characterize dynamical regimes of the system whether it stays in the Floquet-MBL(many-body localization) region or thermalized region. Starting with a product state in the computational basis, followed by reduced density matrix which in turn gives rise to the entanglement entropy density. With the strength of the interaction, the transverse field, the parallel field, the disorder strength W and the driving frequency, we discover the distinct behaviors of fast delocalization and logarithmic entanglement growth and long-lasting memory of the initial state, indicative of localized or prethermal Floquet regimes. We observe that strong disorder arrests transport and enables slow entanglement dynamics, whereas strong driving frequency arrests energy absorption and creates a long-lived non-equilibrium state. Conversely, weak disorder or low driving frequency leads to delocalization. The outcomes show strong support for non-equilibrium phases in driven many-body systems.

arXiv:2606.04976•Jun 3, 2026•0 citations

Quasi-Floquet Prethermalization in a Disordered Dipolar Spin Ensemble in Diamond

G. He, Bingtian Ye, Ruotian Gong +4 more

Floquet (periodic) driving has recently emerged as a powerful technique for engineering quantum systems and realizing nonequilibrium phases of matter. A central challenge to stabilizing quantum phenomena in such systems is the need to prevent energy absorption from the driving field. Fortunately, when the frequency of the drive is significantly larger than the local energy scales of the many-body system, energy absorption is suppressed. The existence of this so-called prethermal regime depends sensitively on the range of interactions and the presence of multiple driving frequencies. Here, we report the observation of Floquet prethermalization in a strongly interacting dipolar spin ensemble in diamond, where the angular dependence of the dipolar coupling helps to mitigate the long-ranged nature of the interaction. Moreover, we extend our experimental observation to quasi-Floquet drives with multiple incommensurate frequencies. In contrast to a single-frequency drive, we find that the existence of prethermalization is extremely sensitive to the smoothness of the applied field. Our results open the door to stabilizing and characterizing nonequilibrium phenomena in quasiperiodically driven systems.

arXiv:2212.11284•Physical Review Letters•Sep 27, 2023•31 citations
We study a periodically driven spin-1/21/21/2 Ising chain with a nearest-neighbour coupling and longitudinal field while a weak transverse field induces single-spin flips. Through Floquet perturbation theory (FPT), we obtain signatures of Hilbert space fragmentation (HSF) and an unconventional form of dynamical localisation which we call the Floquet freezing. Our analysis suggests that these observations emerge due to a single Floquet selection rule that dictates the prethermal dynamics. For a special value of the field-to-interaction strength ratio together with commensurate drive periods, this rule permits only a constrained subset of bulk spin flips, leading to prethermal HSF in the full spin-1/21/21/2 Hilbert space. Under open boundary conditions, the same rule suppresses boundary spin flips up to higher order in perturbation and produces long-lived prethermal edge memory, which is neither topological in origin nor is a strong zero mode. Furthermore, under periodic boundary conditions, the largest surviving fragment is exactly the PXP sector at leading order and therefore exhibits Floquet-inherited scar phenomenology in the prethermal window. At higher commensurate ratios of field strength to interaction strength, all first-order single-spin-flip channels are suppressed and the system enters a regime of Floquet freezing. Hence, our study leverages the selection rules obtained through Floquet perturbation theory to obtain exotic prethermal phenomena at different parameter regimes.
We study the periodic dynamics of a spin-one chain driven using a square-pulse protocol with amplitude Q0Q_0Q0​ and frequency ωDω_DωD​. The Hamiltonian of the spin chain hosts a thermodynamically large number of Z2Z_2Z2​-valued conserved quantities WℓW_{\ell}Wℓ​ on the links ℓ\ellℓ. This allows us to study the Floquet dynamics of this chain within a given sector with fixed values of WℓW_{\ell}Wℓ​. For the sector with all Wℓ=1W_{\ell}=1Wℓ​=1, we find signatures of quantum many-body scar states for ℏωD≫Q0\hbar ω_D \gg Q_0ℏωD​≫Q0​; they lead to oscillatory dynamics and fidelity revival for specific initial states. Upon lowering ωDω_DωD​, we find an ergodic regime exhibiting fast thermalization consistent with the prediction of the (Floquet) eigenstate thermalization hypothesis. In addition, we identify special drive frequencies ωn∗=Q0/(2nℏ)ω_n^{\ast}= Q_0/(2n \hbar)ωn∗​=Q0​/(2nℏ) (where n=1,2,3,⋯n = 1, 2, 3, \cdotsn=1,2,3,⋯) at which the Floquet Hamiltonian exhibits prethermal strong Hilbert space fragmentation (HSF) with the largest fragment being ergodic; in contrast, a weak HSF is found at ωn′=Q0/[ℏ(2n+1)]ω'_n= Q_0/[\hbar(2n+1)]ωn′​=Q0​/[ℏ(2n+1)] (where n=0,1,2,⋯n = 0, 1, 2, \cdotsn=0,1,2,⋯). We also study the sector with Wℓ={⋯1,1,−1,1,1,−1⋯ }W_{\ell} =\{\cdots 1,1,-1,1,1,-1 \cdots \}Wℓ​={⋯1,1,−1,1,1,−1⋯} which shows strong HSF at ωn∗ω_n^{\ast}ωn∗​ but no fragmentation at ωn′ω'_nωn′​. Our analysis indicates that the strong HSF in this sector harbors an integrable largest fragment. We provide numerical support for our analytical and perturbative results using exact-diagonalization (ED) studies on finite chains of length L≤24L\le 24L≤24. Our numerical results for entanglement entropy, fidelity, and correlation functions of the driven chain provide definitive signatures of prethermal strong HSF for both sectors.
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
The concept of Hilbert space fragmentation (HSF) has recently been put forward as a routine to break quantum ergodicity. Although HSF exists widely in models with dynamical constraints, it is still challenging to tune it. Here, we propose a scheme to tune the HSF in a one-dimensional tilted lattice of interacting spinless fermions with periodically driven tunneling. For weak tunneling strength, the dynamics for a long range of time is governed by effective Hamiltonians with kinetic constraints, which appear as density-dependent tunneling. Through a Floquet time-dependent perturbation theory, we analytically derive two different resonance frequencies, at which some particular tunneling processes are resonant. At the nonresonance frequencies, the system is strongly constrained and exhibits a strong HSF. At the two different resonance frequencies, the kinetic constraints are partly released and the system exhibits another two different strong HSFs. We can tune the HSF by changing the driving frequency. We support the perturbation analysis with exact numerical simulation of the entanglement entropy, the density correlation functions, and the saturated local density profiles. Our result provides a promising way to control HSF through Floquet engineering.
We study a fermionic chain with nearest-neighbor hopping and density-density interactions, where the nearest-neighbor interaction term is driven periodically. We show that such a driven chain exhibits prethermal strong Hilbert space fragmentation (HSF) in the high drive amplitude regime at specific drive frequencies ω_{m}^{*}. This constitutes the first realization of HSF for out-of-equilibrium systems. We obtain analytic expressions of ω_{m}^{*} using a Floquet perturbation theory and provide exact numerical computation of entanglement entropy, equal-time correlation functions, and the density autocorrelation of fermions for finite chains. All of these quantities indicate clear signatures of strong HSF. We study the fate of the HSF as one tunes away from ω_{m}^{*} and discuss the extent of the prethermal regime as a function of the drive amplitude.
We study the non-equilibrium dynamics of a disordered periodically driven quantum spin chain, with the competition between the interaction, disorder, and Floquet driving being of particular interest. We study dynamics of entanglement entropy, energy absorption to characterize dynamical regimes of the system whether it stays in the Floquet-MBL(many-body localization) region or thermalized region. Starting with a product state in the computational basis, followed by reduced density matrix which in turn gives rise to the entanglement entropy density. With the strength of the interaction, the transverse field, the parallel field, the disorder strength W and the driving frequency, we discover the distinct behaviors of fast delocalization and logarithmic entanglement growth and long-lasting memory of the initial state, indicative of localized or prethermal Floquet regimes. We observe that strong disorder arrests transport and enables slow entanglement dynamics, whereas strong driving frequency arrests energy absorption and creates a long-lived non-equilibrium state. Conversely, weak disorder or low driving frequency leads to delocalization. The outcomes show strong support for non-equilibrium phases in driven many-body systems.
Floquet (periodic) driving has recently emerged as a powerful technique for engineering quantum systems and realizing nonequilibrium phases of matter. A central challenge to stabilizing quantum phenomena in such systems is the need to prevent energy absorption from the driving field. Fortunately, when the frequency of the drive is significantly larger than the local energy scales of the many-body system, energy absorption is suppressed. The existence of this so-called prethermal regime depends sensitively on the range of interactions and the presence of multiple driving frequencies. Here, we report the observation of Floquet prethermalization in a strongly interacting dipolar spin ensemble in diamond, where the angular dependence of the dipolar coupling helps to mitigate the long-ranged nature of the interaction. Moreover, we extend our experimental observation to quasi-Floquet drives with multiple incommensurate frequencies. In contrast to a single-frequency drive, we find that the existence of prethermalization is extremely sensitive to the smoothness of the applied field. Our results open the door to stabilizing and characterizing nonequilibrium phenomena in quasiperiodically driven systems.