Discrete time-crystalline response stabilized by domain-wall confinement

TL;DR

This paper demonstrates that domain-wall confinement in clean quantum spin chains can stabilize discrete time-crystalline order, with interaction range playing a crucial role in exponentially increasing the lifetime of the order.

Contribution

It introduces a novel mechanism for stabilizing time crystals via domain-wall confinement in clean systems, independent of disorder or Floquet prethermalization.

Findings

Confinement effects can be averaged out by periodic driving, leading to deconfined dynamics.

Increasing interaction range exponentially enhances the lifetime of the order parameter.

The stability of the time crystal does not rely on eigenstate order or prethermalization.

Abstract

Discrete time crystals represent a paradigmatic nonequilibrium phase of periodically driven matter. Protecting its emergent spatiotemporal order necessitates a mechanism that hinders the spreading of defects, such as localization of domain walls in disordered quantum spin chains. In this work, we establish the effectiveness of a different mechanism arising in clean spin chains: the confinement of domain walls into ``mesonic'' bound states. We consider translationally invariant quantum Ising chains periodically kicked at arbitrary frequency, and discuss two possible routes to domain-wall confinement: longitudinal fields and interactions beyond nearest neighbors. We study the impact of confinement on the order parameter evolution by constructing domain-wall-conserving effective Hamiltonians and analyzing the resulting dynamics of domain walls. On the one hand, we show that for arbitrary driving frequency the symmetry-breaking-induced confining potential gets effectively averaged out by the drive, leading to deconfined dynamics. On the other hand, we rigorously prove that increasing the range $R$ of spin-spin interactions $J_{i,j}$ beyond nearest neighbors enhances the order-parameter lifetime \textit{exponentially} in $R$. Our theory predictions are corroborated by a combination of exact and matrix-product-state simulations for finite and infinite chains, respectively. The long-lived stability of spatiotemporal order identified in this work does not rely on Floquet prethermalization nor on eigenstate order, but rather on the nonperturbative origin of vacuum-decay processes. We point out the experimental relevance of this new mechanism for stabilizing a long-lived time-crystalline response in Rydberg-dressed spin chains.