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

Abstract

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

18 pages, 11 figures