Floquet time crystals in driven spin systems with all-to-all p -body interactions
Floquet time crystals in driven spin systems with all-to-all p -body interactions
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DOI：
10.1103/physrevresearch.4.023018
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发表时间：
2022-01
影响因子：
4.2
通讯作者：
M. Muñoz-Arias;K. Chinni;P. Poggi
中科院分区：
文献类型：
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作者：
M. Muñoz-Arias;K. Chinni;P. Poggi
我们展示了周期性驱动的 p 自旋模型的 Floquet 动力学中 Floquet 时间晶体 (FTC) 相的出现，该模型描述了具有所有 p 体相互作用的自旋 1/2 粒子的集合。考虑到这些模型的平均场性质，我们精确地在热力学极限内处理该问题，并表明，对于给定的 p ，这些系统可以承载周期为 nT 的各种鲁棒时间晶体响应，其中 T 是驱动周期，n 是 2 和 p 之间的整数。特别是，四体相互作用（p = 4）的情况产生了常见的倍周期晶体，以及新颖的四倍周期相。我们开发了一个综合框架来预测经典保面积图中的鲁棒次谐波响应，并以此为基础来预测量子态中平均场 FTC 相位的发生并表征其稳定性。我们的分析表明，时间晶体行为的鲁棒性随着周期的增加而降低，并在由本征态有序和稳健的次谐波响应描述的时间晶体的出现与激发态和动态量子相变的现象学之间建立了联系。最后，对于包含两个或多个共存时间晶体相的模型，我们定义了协议，其中系统的周期性分谐波响应可以通过外部控制参数的非周期性调制随时间变化。
We show the emergence of Floquet time crystal (FTC) phases in the Floquet dynamics of periodically driven p -spin models, which describe a collection of spin-1/2 particles with all-to-all p -body interactions. Given the mean-field nature of these models, we treat the problem exactly in the thermodynamic limit and show that, for a given p , these systems can host various robust time-crystalline responses with period nT , where T is the period of the drive and n an integer between 2 and p . In particular, the case of four-body interactions ( p = 4) gives rise to both a usual period-doubling crystal, and also a novel period-quadrupling phase. We develop a comprehensive framework to predict robust subharmonic response in classical area-preserving maps, and use this as a basis to predict the occurrence and characterize the stability of the resulting mean-field FTC phases in the quantum regime. Our analysis reveals that the robustness of the time-crystal behavior is reduced as their period increases, and establishes a connection between the emergence of time crystals, described by eigenstate ordering and robust subharmonic response, and the phenomenology of excited state and dynamical quantum phase transitions. Finally, for the models hosting two or more coexisting time crystal phases, we define protocols where the periodic subharmonic response of the system can be varied in time via the non-periodic modulation of an external control parameter.