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 we 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 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.

中文翻译：

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域壁约束稳定的离散时间-晶体响应

离散时间晶体代表了周期性驱动物质的典型非平衡阶段。保护其出现的时空顺序需要一种阻碍缺陷扩散的机制，例如无序量子自旋链中畴壁的定位。在这项工作中，我们确定了在干净自旋链中产生的不同机制的有效性：将畴壁限制在“介子”束缚态中。我们考虑以任意频率周期性地踢的平移不变的量子伊辛链，我们讨论了两种可能的畴壁限制途径：纵向场和最近邻之外的相互作用。我们通过构造畴壁守恒的有效哈密顿量并分析畴壁的最终动力学来研究约束对阶参数演化的影响。一方面，我们表明，对于任意驱动频率，对称破缺引起的限制电位被驱动有效地平均化，导致动力学解除。另一方面，我们严格证明增加范围$R$自旋-自旋相互作用${Ĵ}_{\mathrm{一世},j}$超越最近邻会以指数方式增强顺序参数的寿命$R$. 我们的理论预测分别通过有限链和无限链的精确和矩阵乘积状态模拟的组合得到证实。在这项工作中确定的时空有序的长期稳定性不依赖于 Floquet 预热化或本征态序，而是依赖于真空衰减过程的非微扰起源。我们指出了这种新机制的实验相关性，用于稳定里德堡修饰的自旋链中的长寿命时间晶体响应。