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

TL;DR

This paper investigates the driven spin-one chain's Floquet dynamics, revealing quantum many-body scars, ergodic regimes, and prethermal Hilbert space fragmentation at specific drive frequencies, supported by numerical exact-diagonalization studies.

Contribution

It uncovers novel prethermal fragmentation phenomena and quantum scars in a driven spin-one chain, with analytical and numerical evidence for frequency-dependent ergodic and non-ergodic phases.

Findings

Identification of Floquet scars leading to oscillatory dynamics and fidelity revival.

Discovery of special drive frequencies causing prethermal Hilbert space fragmentation.

Numerical evidence of entanglement entropy and correlation signatures of these phenomena.

Abstract

We study the periodic dynamics of a spin-one chain driven using a square-pulse protocol with amplitude $Q_0$ and frequency $\omega_D$. 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 $\hbar \omega_D \gg Q_0$; they lead to oscillatory dynamics and fidelity revival for specific initial states. Upon lowering $\omega_D$, 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 $\omega_n^{\ast}= Q_0/(2n \hbar)$ (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 $\omega'_n= Q_0/[\hbar(2n+1)]$ (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 $\omega_n^{\ast}$ but no fragmentation at $\omega'_n$. 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.