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Discrete time-crystalline response stabilized by domain-wall confinement

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.