[论文解读] A Brief History of Time Crystals

Vedika Khemani, Roderich Moessner+1 more|arXiv (Cornell University)|Oct 23, 2019

Quantum many-body systems参考文献 18被引用 120

一句话总结

一篇全面综述，论证在周期驱动的、多体局域化量子系统中会发生离散时间-平移对称性破缺，定义 Floquet 时间晶体，并详细介绍它们的诊断、理论与实验。

ABSTRACT

The idea of breaking time-translation symmetry has fascinated humanity at least since ancient proposals of the perpetuum mobile. Unlike the breaking of other symmetries, such as spatial translation in a crystal or spin rotation in a magnet, time translation symmetry breaking (TTSB) has been tantalisingly elusive. We review this history up to recent developments which have shown that discrete TTSB does takes place in periodically driven (Floquet) systems in the presence of many-body localization. Such Floquet time-crystals represent a new paradigm in quantum statistical mechanics --- that of an intrinsically out-of-equilibrium many-body phase of matter. We include a compendium of necessary background, before specializing to a detailed discussion of the nature, and diagnostics, of TTSB. We formalize the notion of a time-crystal as a stable, macroscopic, conservative clock --- explaining both the need for a many-body system in the infinite volume limit, and for a lack of net energy absorption or dissipation. We also cover a range of related phenomena, including various types of long-lived prethermal time-crystals, and expose the roles played by symmetries -- exact and (emergent) approximate -- and their breaking. We clarify the distinctions between many-body time-crystals and other ostensibly similar phenomena dating as far back as the works of Faraday and Mathieu. En route, we encounter Wilczek's suggestion that macroscopic systems should exhibit TTSB in their ground states, together with a theorem ruling this out. We also analyze pioneering recent experiments detecting signatures of time crystallinity in a variety of different platforms, and provide a detailed theoretical explanation of the physics in each case. In all existing experiments, the system does not realize a `true' time-crystal phase, and we identify necessary ingredients for improvements in future experiments.

研究动机与目标

• 明确量子系统中时间平移对称性破缺的概念与定义
• 解释为何时间晶体需要非平衡、多体设定与无限系统极限
• 综述 Floquet 多体局域化时间晶体及其诊断工具
• 讨论预热时间晶体与对称性保护时间晶体作为拓展
• 评审实验实现及其理论解释，略。

提出的方法

• 在多体系统中提供时间平移对称性破缺与时空序的精确定义
• 讨论周期驱动下防止加热的多体局域化作用
• 提出 TTSB 的诊断工具，包括时间/时空序与易感性
• 分析具体的 Floquet 伊辛型模型和 π 自旋-玻璃相，作为时晶体的具体实现
• 综述预热和对称性保护时间晶体，作为超越理想 Floquet MBL 系统的拓展
• 在各平台比较理论预测与实验观测

实验结果

研究问题

• RQ1 在量子多体系统中，什么构成对时间平移对称性破缺的严格定义？
• RQ2 在何种条件下，周期驱动（Floquet）系统能在不加热的情况下实现稳定时间晶体？
• RQ3 多体局域化与湧现的守恒量如何使 Floquet 时间晶体成为可能？
• RQ4 在本征态与动力学中，TTSB 与时空序的诊断性特征是什么？
• RQ5 预热与对称性保护时间晶体如何扩展或修改 Floquet MBL 框架？

主要发现

• 离散时间-平移对称性破缺可以在多体局域化的 Floquet 系统中发生，产生一个稳定的、宏观的时钟。
• 时间晶体表现出时空序，在某些相（如 π 自旋-玻璃）中破坏离散时间平移和空间对称性。
• 诊断工具如时间与时空序、易感性以及非平凡的晚期演化对于识别 TTSB 至关重要。
• 在量子离子陷阱、NV 中心和 NMR 平台上的实验实现显示出与时晶体物理相符的信号，尽管真正的渐近时间晶体仍然具有挑战性。
• 预热时间晶体和对称性保护时间晶体拓展了超越理想 Floquet MBL 时间晶体的范围。