标题： 一种节拍器自旋稳定时间晶体动力学 显示英文标题

标题： A metronome spin stabilizes time-crystalline dynamics

摘要： 我们研究了一个无无序的量子伊辛链，该链受到一个时间周期性驱动，使每个自旋旋转一个角度$\pi(1-\epsilon_i)$。 在所有自旋经历相同的偏差$\epsilon$的情况下，系统初始化为完全极化的状态，其动力学已知为时间晶体：系统的磁化率在随链长度指数增长的时间尺度上表现出周期加倍的振荡。 在本工作中，我们研究了在自旋之间不同的偏差$\epsilon$的影响。 我们发现，对单个自旋减少$\epsilon$可显著增强时空序的寿命，这表明其名称为“节拍器”自旋。 通过平均哈密顿量图景中的微扰论论证，我们解释了具有宏观体磁化的初始状态的这一观察结果。 此外，在随机位串初始状态下，我们报告了拓扑边缘模寿命的增强，这也可以在同一图景中理解。 最后，我们讨论了一种改变的几何结构，在这种结构中，“节拍器”自旋不是链的直接组成部分，它在所考虑的两种情景中以不同的方式影响动力学。 我们的发现揭示了在空间变化驱动影响下弗洛凯系统中出现的复杂动力学，从而揭示了弗洛凯工程的新途径。 显示英文摘要

摘要： We investigate a disorder-free quantum Ising chain subject to a time-periodic drive that rotates each spin by an angle $\pi(1-\epsilon_i)$. In case all spins experience the same deviation $\epsilon$ and the system is initialized in a fully polarized state, the dynamics is known to be time-crystalline: the magnetization of the system exhibits period-doubled oscillations for timescales that grow exponentially with the length of the chain. In this work, we study the effect of a deviation $\epsilon$ that differs between spins. We find that reducing $\epsilon$ for a single spin drastically enhances the lifetime of spatio-temporal order, suggesting the name ``metronome" spin. Employing perturbative arguments in an average Hamiltonian picture, we explain this observation for initial states with macroscopic bulk magnetization. Furthermore, in the case of random bitstring initial states, we report the enhancement of the lifetime of a topological edge mode, which can also be understood in the same picture. Finally, we discuss an altered geometry in which the metronome spin is not directly part of the chain, affecting the dynamics in different ways in the two scenarios considered. Our findings unveil the intricate dynamics that emerge in Floquet systems under the influence of a spatially varying drive, thereby uncovering new avenues for Floquet engineering.