Prethermal fragmentation in a periodically driven Fermionic chain

TL;DR

This paper demonstrates the first out-of-equilibrium realization of Hilbert space fragmentation in a periodically driven Fermionic chain, revealing a prethermal regime with strong fragmentation at specific drive frequencies.

Contribution

It provides analytic expressions for the critical drive frequencies and numerical evidence of strong Hilbert space fragmentation in a driven Fermionic system.

Findings

Identification of specific drive frequencies $\u00a0_m^{a0}$ where HSF occurs

Exact numerical signatures of HSF in entanglement and correlation functions

Prethermal regime extent depends on drive amplitude

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 $\omega_m^{\ast}$. This constitutes the first realization of HSF for out-of-equilibrium systems. We obtain analytic expressions of $\omega_m^{\ast}$ 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 $\omega_m^{\ast}$ and discuss the extent of the prethermal regime as a function of the drive amplitude.