The spontaneous breaking of time-translation symmetry has led to the discovery of a new phase of matter: the discrete time crystal. Discrete time crystals exhibit rigid subharmonic oscillations that result from a combination of many-body interactions, collective synchronization, and ergodicity breaking. This Colloquium reviews recent theoretical and experimental advances in the study of quantum and classical discrete time crystals. The breaking of ergodicity is focused upon as the key to discrete time crystals and the delaying of ergodicity as the source of numerous phenomena that share many of the properties of discrete time crystals, including the ac Josephson effect, coupled map lattices, and Faraday waves. Theoretically, there is a diverse array of strategies to stabilize time-crystalline order in both closed and open systems, ranging from localization and prethermalization to dissipation and error correction. Experimentally, many-body quantum simulators provide a natural platform for investigating signatures of time-crystalline order; recent work utilizing trapped ions, solid-state spin systems, and superconducting qubits are reviewed. Finally, this Colloquium concludes by describing outstanding challenges in the field and a vision for new directions on both the experimental and theoretical fronts.

中文翻译：

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座谈会：量子和经典离散时间晶体

时间平移对称性的自发破缺导致了物质新相的发现：离散时间晶体。离散时间晶体表现出刚性次谐波振荡，这是由多体相互作用、集体同步和遍历性破坏的组合产生的。本次研讨会回顾了量子和经典离散时间晶体研究的最新理论和实验进展。遍历性的破坏被视为离散时间晶体的关键，而遍历性的延迟被视为许多现象的根源，这些现象共享离散时间晶体的许多属性，包括交流约瑟夫森效应、耦合映射晶格和法拉第波。理论上，在封闭和开放系统中，有多种策略可以稳定时间晶体秩序，从局域化和预热到耗散和误差校正。在实验上，多体量子模拟器为研究时间晶体秩序的特征提供了一个自然的平台；回顾了最近利用捕获离子、固态自旋系统和超导量子位的工作。最后，本次研讨会通过描述该领域的突出挑战以及实验和理论前沿新方向的愿景来结束。