Discrete time crystals enabled by Floquet strong Hilbert space fragmentation

TL;DR

This paper demonstrates that Floquet strong Hilbert space fragmentation can stabilize discrete time crystals in a disorder-free quantum spin chain, revealing multiple-period responses and exponential lifetime growth with system size.

Contribution

It introduces a disorder-free mechanism for stabilizing discrete time crystals via Floquet Hilbert space fragmentation, with analytical and numerical validation.

Findings

Period-doubling response of DTC order confirmed numerically.

Multiple-period beating dynamics observed due to $\pi$-pair interplay.

DTC lifetime grows exponentially with system size, independent of driving frequency.

Abstract

Discrete time crystals (DTCs) are non-equilibrium phases of matter that break the discrete time-translation symmetry and is characterized by a robust subharmonic response in periodically driven quantum systems. Here, we explore the DTC in a disorder-free, periodically kicked XXZ spin chain, which is stabilized by the Floquet strong Hilbert space fragmentation. We numerically show the period-doubling response of the conventional DTC order, and uncover a multiple-period response with beating dynamics due to the coherent interplay of multiple $\pi$-pairs in the Floquet spectrum of small-size systems. The lifetime of the DTC order exhibits independence of the driving frequency and a power-law dependence on the ZZ interaction strength. It also grows exponentially with the system size, as a hallmark of the strong fragmentation inherent to the Floquet model. We analytically reveal the approximate conservation of the magnetization and domain-wall number in the Floquet operator for the emergent strong fragmentation, which is consistent with numerical results of the dimensionality ratio of symmetry subspaces. The rigidity and phase regime of the DTC order are identified through finite-size scaling of the Floquet-spectrum-averaged mutual information, as well as via dynamical probes. Our work establishes the Floquet Hilbert space fragmentation as a disorder-free mechanism for sustaining nontrivial temporal orders in out-of-equilibrium quantum many-body systems.