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arXiv:2212.03892 · Physical Review Letters

Prethermal Fragmentation in a Periodically Driven Fermionic Chain

Somsubhra Ghosh, Indranil Paul, K. Sengupta

Published Mar 23, 2023• 23 citations
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Abstract

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.

DOI
10.1103/physrevlett.130.120401

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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.
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The occurrence of prethermal Hilbert space fragmentation (HSF) in periodically driven quantum systems has its roots in the emergence of additional, approximate, kinetic constraints at special driving frequencies. Here, the authors show that the out-of-time-ordered correlators (OTOCs) of a driven fermion chain with open boundary condition exhibit a signature of such HSF. At the special drive frequencies where such prethermal HSF occurs, the OTOCs display periodic unscrambling of information, which provides a yet unexplored, experimentally testable, marker for prethermal fragmentation.
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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.
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