Pizzi Andrea, Knolle Johannes, Nunnenkamp Andreas
Cavendish Laboratory, University of Cambridge, Cambridge, UK.
Department of Physics, Technische Universität München, Garching, Germany.
Nat Commun. 2021 Apr 20;12(1):2341. doi: 10.1038/s41467-021-22583-5.
Discrete time crystals are periodically driven systems characterized by a response with periodicity nT, with T the period of the drive and n > 1. Typically, n is an integer and bounded from above by the dimension of the local (or single particle) Hilbert space, the most prominent example being spin-1/2 systems with n restricted to 2. Here, we show that a clean spin-1/2 system in the presence of long-range interactions and transverse field can sustain a huge variety of different 'higher-order' discrete time crystals with integer and, surprisingly, even fractional n > 2. We characterize these (arguably prethermal) non-equilibrium phases of matter thoroughly using a combination of exact diagonalization, semiclassical methods, and spin-wave approximations, which enable us to establish their stability in the presence of competing long- and short-range interactions. Remarkably, these phases emerge in a model with continous driving and time-independent interactions, convenient for experimental implementations with ultracold atoms or trapped ions.
离散时间晶体是周期性驱动系统，其特征在于具有周期为nT的响应，其中T是驱动周期且n>1。通常，n是整数且上限由局部（或单粒子）希尔伯特空间的维度确定，最突出的例子是自旋1/2系统，其中n限于2。在此，我们表明，在存在长程相互作用和横向场的情况下，一个纯净的自旋1/2系统可以维持各种各样不同的“高阶”离散时间晶体，n为整数，令人惊讶的是，甚至有分数n>2。我们通过精确对角化、半经典方法和自旋波近似相结合的方式，全面地对这些（可以说是预热的）非平衡物质相进行了表征，这使我们能够在存在竞争的长程和短程相互作用的情况下确定它们的稳定性。值得注意的是，这些相出现在一个具有连续驱动和与时间无关的相互作用的模型中，这便于用超冷原子或捕获离子进行实验实现。
