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arXiv:2603.06111

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

Krishanu Ghosh, Diptiman Sen, K. Sengupta

cond-mat.stat-mechquant-phSubmitted Mar 6, 2026• Announced Mar 9, 2026• 0 citations
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Abstract

We study the periodic dynamics of a spin-one chain driven using a square-pulse protocol with amplitude $Q_0$ and frequency $ω_D$. 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 $\hbar ω_D \gg Q_0$; 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 $ω_n^{\ast}= Q_0/(2n \hbar)$ (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 $ω'_n= Q_0/[\hbar(2n+1)]$ (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 $ω_n^{\ast}$ 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 $L\le 24$. Our numerical results for entanglement entropy, fidelity, and correlation functions of the driven chain provide definitive signatures of prethermal strong HSF for both sectors.

Comments
18 pages, 11 figures

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We investigate the emergence of a scarred discrete time crystal (SDTC) phase in a periodically driven dimerized spin chain. While generic interacting Floquet systems are expected to thermalize according to the eigenstate thermalization hypothesis (ETH), we demonstrate that this system hosts quantum many-body scars (QMBS) that induce a regime of weak ergodicity breaking. Through an analysis of Floquet level statistics, entanglement entropy, and eigenstate fidelity, we identify a manifold of low-entanglement states characterized by semi-Poisson statistics embedded within an otherwise thermal spectrum. These scarred states support robust subharmonic oscillations with period doubling, signaling the spontaneous breaking of discrete time-translation symmetry. We show that the SDTC response is robust against a variety of initial state configurations, demonstrating its stability beyond fine-tuned conditions. A finite-size scaling analysis reveals that the time-crystalline lifetime grows with system size within the range accessible to our exact-diagonalization calculations. However, drawing on the general phenomenology of approximate many-body scars, we expect that hybridization between Floquet scars and the thermal continuum will eventually curtail this growth, causing the lifetime to saturate at system sizes beyond our current numerical reach. This characterizes the SDTC as a long-lived metastable dynamical regime rather than a strictly stable thermodynamic phase, providing a comprehensive framework for understanding the interplay between periodic driving and constrained many-body dynamics in disorder-free systems.
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