Experimental advances have allowed for the exploration of nearly isolated quantum many-body systems whose coupling to an external bath is very weak. A particularly interesting class of such systems is those which do not thermalize under their own isolated quantum dynamics. In this review, we highlight the possibility for such systems to exhibit new non-equilibrium phases of matter. In particular, we focus on "discrete time crystals", which are many-body phases of matter characterized by a spontaneously broken discrete time translation symmetry. We give a definition of discrete time crystals from several points of view, emphasizing that they are a non-equilibrium phenomenon, which is stabilized by many-body interactions, with no analog in non-interacting systems. We explain the theory behind several proposed models of discrete time crystals, and compare a number of recent realizations, in different experimental contexts.
Classical approaches to prethermal discrete time crystals in one, two, and three dimensions
我们提供了经典汉密尔顿动力学中预热离散时间晶体的全面描述，补充和扩展了我们最近的工作[Phys. Rev. Lett. 127，140602（2021）]。考虑到幂律相互作用自旋一维，二维和三维超立方晶格，我们调查的维度和相互作用范围之间的相互作用，在这些非平衡阶段的物质，打破了离散的时间平移对称性的周期性驱动器的稳定。
Discrete time crystal for periodic-field sensing with quantum-enhanced precision
Qatar Center for Quantum Computing, College of Science and Engineering, Hamad Bin Khalifa University（卡塔尔量子计算中心，科学与工程学部，哈马德·本·哈利法大学）；Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China（前沿科学与基础研究院，电子科技大学）；Key Laboratory of Quantum Physics and Photonic Quantum Information, Ministry of Education, University of Electronic Science and Technology of China（教育部量子物理与光量子信息重点实验室，电子科技大学）
Reply to Comment on "Discrete Time Crystals: Rigidity Criticality and Realizations"
这是对Khemani，Moessner和Sondhi（KMS）[arXiv：2109.00551]对我们手稿[Phys. Rev. Lett. 118，030401（2017）]。KMS中的主要新声明是短程模型不支持MBL DTC阶段。我们表明，即使对于他们考虑的参数值和他们研究的系统大小，索赔是一个不寻常的选择范围的关键情节的神器。对相同的数据进行标准的有限尺寸标度分析强烈表明，该系统实际上是一个多体定域（MBL）离散时间晶体（DTC）。此外，我们还在更大的尺度上进行了额外的模拟，并提供了一个分析论证，完全支持我们原始论文的结论。我们还表明，边界条件的影响，描述为必不可少的KMS，正是人们所期望的，随着系统尺寸的增加，边界效应降低。KMS中的其他点要么是文献中已有的点（对于长期模型）的重新整理，要么被适当的有限尺寸标度分析所反驳。
Nonlinearity-enhanced Quantum Sensing in Discrete Time Crystal Probes
Qatar Center for Quantum Computing, College of Science and Engineering, Hamad Bin Khalifa University（卡塔尔量子计算中心，科学与工程学院，哈马德·本·哈利法大学）；Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China（前沿科学学院，电子科技大学）；Key Laboratory of Quantum Physics and Photonic Quantum Information, Ministry of Education, University of Electronic Science and Technology of China（教育部量子物理与光子量子信息重点实验室，电子科技大学）；Shimmer Center, Tianfu Jiangxi Laboratory（shimmer 中心，天府江西实验室）
A Robust Large-Period Discrete Time Crystal and its Signature in a Digital Quantum Computer
Bioinformatics Institute, Agency for Science, Technology and Research (A*STAR)（生物信息学研究所，科学与技术研究局（A*STAR））；Department of Physics, National University of Singapore（新加坡国立大学物理系）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；School of Physical and Mathematical Sciences, Nanyang Technological University（南洋理工大学物理与数学科学学院）；Institute of High Performance Computing (IHPC), Agency for Science, Technology and Research (A*STAR)（高性能计算研究所（IHPC），科学与技术研究局（A*STAR））；Department of Physics, Interdisciplinary Research Center for Intelligent Secure Systems, King Fahd University of Petroleum and Minerals（阿卜杜拉国王科技大学物理系，智能安全系统跨学科研究中心）
