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

We study the periodic dynamics of a spin-one chain driven using a square-pulse protocol with amplitude Q₀ and frequency ω_D. The Hamiltonian of the spin chain hosts a thermodynamically large number of Z₂-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 Q₀; 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= Q₀/\(2n hbar\) 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= Q₀/\[hbar(2n+1)\] 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 Lle 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.