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A discrete time crystal (DTC) repeats itself with a rigid rhythm, mimicking a ticking clock set by the interplay between its internal structures and an external force. DTCs promise profound applications in precision time-keeping and other…

Quantum Gases · Physics 2020-07-22 Changyuan Lyu , Sayan Choudhury , Chenwei Lv , Yangqian Yan , Qi Zhou

Time crystals are classified into discrete time crystals and continuous time crystals based on whether they spontaneously break time-translation symmetry. Continuous-time crystals do not require external driving. By introducing AdS/CFT…

Quantum Physics · Physics 2025-08-15 Ximo Wang , Qiwei Han , Zhenqi Bai , Hongyan Fan , Yichi Zhang

A discrete time crystal (DTC) is the paradigmatic example of a phase of matter that occurs exclusively in systems out of equilibrium. This phenomenon is characterized by the spontaneous symmetry breaking of discrete time-translation and…

We introduce a new class of out-of-equilibrium noninteracting topological phases, the topological space-time crystals. These are time-dependent quantum systems which do not have discrete spatial translation symmetries, but instead are…

Mesoscale and Nanoscale Physics · Physics 2022-05-06 Yang Peng

Time crystals in periodically driven systems have initially been studied assuming either the ability to quench the Hamiltonian between different many-body regimes, the presence of disorder or long-range interactions. Here we propose the…

Pair interaction potentials between atoms in a crystal are in general non-monotonic in distance, with a local minimum whose position gives the lattice constant of the crystal. A temporal analogue of this idea of crystal formation is still…

Atomic Physics · Physics 2025-05-01 Weiyu Wang , Mingjun Feng , Qianjin Ma , Zi Cai , Erwei Li , Guobin Liu

Investigation of states with a periodic time dependence of physical quantities attracts a considerable interest now. Although it has been proposed initially that such states (coined Quantum Time Crystals) might be macroscopic and…

Strongly Correlated Electrons · Physics 2019-11-07 Konstantin B. Efetov

Time crystals appear when systems display a commensurate spontaneous breaking of the discrete time translational invariance imposed by an external periodic drive. No consensus on the definition has been reached as yet, but important aspects…

Statistical Mechanics · Physics 2023-01-18 Robin Schäfer , Götz S. Uhrig , Joachim Stolze

Spontaneous symmetry breaking is a fundamental concept in many areas of physics, ranging from cosmology and particle physics to condensed matter. A prime example is the breaking of spatial translation symmetry, which underlies the formation…

Time crystals are classified as discrete or continuous depending on whether they spontaneously break discrete or continuous time translation symmetry. While discrete time crystals have been extensively studied in periodically driven systems…

Time crystals are genuinely non-equilibrium quantum phases of matter that break time-translational symmetry. While in non-equilibrium closed systems time crystals have been experimentally realized, it remains an open question whether or not…

Quantum Physics · Physics 2020-05-27 Andreu Riera-Campeny , Maria Moreno-Cardoner , Anna Sanpera

A time crystal is a time dependent physical system that does not reach a standstill, even in state of minimum energy. Here we show that the stability of a time crystal can be enhanced by its topology. For this we simulate time crystals made…

Pattern Formation and Solitons · Physics 2019-10-31 Jin Dai , Xubiao Peng , Antti J. Niemi

Time crystals, as temporal analogs of space crystals, manifest as stable and periodic behavior that breaks time translation symmetry. In an open quantum system, many-body interaction subjected to dissipation allows one to develop the time…

Atomic Physics · Physics 2025-10-09 Yuechun Jiao , Weilun Jiang , Yu Zhang , Jingxu Bai , Yunhui He , Heng Shen , Jianming Zhao , Suotang Jia

Spontaneous symmetry breaking is one of the central organizing principles in physics. Time crystals have emerged as an exotic phase of matter, spontaneously breaking the time translational symmetry, and are mainly categorized as discrete or…

Quantum Physics · Physics 2026-01-16 Jan Carlo Schumann , Igor Lesanovsky , Parvinder Solanki

Periodically-driven open quantum systems that never thermalize exhibit a discrete time-crystal behavior, a non-equilibrium quantum phenomenon that has shown promise in quantum information processing applications. Measurements of…

Mesoscale and Nanoscale Physics · Physics 2023-07-11 Subhajit Sarkar , Yonatan Dubi

Time crystals are a phase of matter, for which the discrete time symmetry of the driving Hamiltonian is spontaneously broken. The breaking of discrete time symmetry has been observed in several experiments in driven spin systems. Here, we…

Quantum Gases · Physics 2018-11-07 Jasper Smits , Lei Liao , Henk Stoof , Peter van der Straten

Time crystals are an eagerly sought phase of matter with broken time-translation symmetry. Quantum time crystals with discretely broken time-translation symmetry have been demonstrated in trapped ions, atoms and spins while continuously…

Optics · Physics 2023-08-03 Tongjun Liu , Jun-Yu Ou , Kevin F. MacDonald , Nikolay I. Zheludev

Time crystals are many-body systems that spontaneously break time-translation symmetry, and thus exhibit long-range spatiotemporal order and robust periodic motion. Recent results have demonstrated how to build time-crystal phases in driven…

Statistical Mechanics · Physics 2025-04-11 R. Hurtado-Gutiérrez , C. Pérez-Espigares , P. I. Hurtado

Time crystal is a class of non-equilibrium phases with broken time-translational symmetry. Here we demonstrate the time crystal in a single-mode nonlinear cavity. The time crystal originates from the self-oscillation induced by a linear…

Quantum Physics · Physics 2024-12-05 Yaohua Li , Chenyang Wang , Yuanjiang Tang , Yong-Chun Liu

A time crystal is an exotic phase of matter where time-translational symmetry is broken; this phase differs from the spatial symmetry breaking induced in crystals in space. Lots of experiments report the transition from a thermal…