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Time crystals are proposed states of matter which spontaneously break time translation symmetry. There is no settled definition of such states. We offer a new definition which follows the traditional recipe for Wigner symmetries and order…

Statistical Mechanics · Physics 2017-09-27 Vedika Khemani , C. W. von Keyserlingk , S. L. Sondhi

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

We show that interacting bosons on a ring which are driven periodically by a rotating potential can support discrete time crystals whose absolute stability can be proven. The absolute stability is demonstrated by an exact mapping of…

Quantum Gases · Physics 2023-11-29 Krzysztof Giergiel , Jia Wang , Bryan J. Dalton , Peter Hannaford , Krzysztof Sacha

Understanding how temporal order degrades in quantum systems remains a central issue in nonequilibrium physics. Here we study the melting of discrete time crystals in a periodically driven holographic system, where a distinct (discrete)…

High Energy Physics - Theory · Physics 2026-04-16 Yu-Qi Lei , Xian-Hui Ge , Yu Tian , Shao-Feng Wu

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

Between space crystals and amorphous materials there exists a third class of aperiodic structures which lack translational symmetry but reveal long-range order. They are dubbed quasi-crystals and their formation, similarly as the formation…

Quantum Gases · Physics 2019-06-19 Krzysztof Giergiel , Arkadiusz Kuroś , Krzysztof Sacha

Time crystals are quantum systems which are able to reveal condensed matter behavior in the time domain. It is known that crystalization in time can be observed in a periodically driven many-body system when interactions between particles…

Quantum Gases · Physics 2019-04-02 Pawel Matus , Krzysztof Sacha

Discrete time-crystals are periodically driven quantum many-body systems with broken discrete-time translational symmetry, a non-equilibrium steady state representing self-organization of motion of quantum particles. Observations of…

Mesoscale and Nanoscale Physics · Physics 2022-06-28 Subhajit Sarkar , Yonatan Dubi

Motivated by experimental observations of time-symmetry breaking behavior in a periodically driven (Floquet) system, we study a one-dimensional spin model to explore the stability of such Floquet discrete time crystals (DTCs) under the…

Strongly Correlated Electrons · Physics 2017-09-25 Tian-Sheng Zeng , D. N. Sheng

Discrete time crystals are a recently proposed and experimentally observed out-of-equilibrium dynamical phase of Floquet systems, where the stroboscopic evolution of a local observable repeats itself at an integer multiple of the driving…

Statistical Mechanics · Physics 2018-01-29 Zongping Gong , Ryusuke Hamazaki , Masahito Ueda

Discrete time crystals (DTCs) are nonequilibrium phases of matter characterized by robust subharmonic order parameter dynamics. We report a new type of DTC in a periodically driven surface code, the subharmonic signature of which is only…

Quantum Physics · Physics 2021-08-04 Raditya Weda Bomantara

Periodically driven quantum systems manifest various non-equilibrium features which are absent at equilibrium. For example, discrete time-translation symmetry can be broken in periodically driven quantum systems leading to an exotic phase…

Quantum Physics · Physics 2020-04-09 C. M. Dai , Z. C. Gu , X. X. Yi

Time crystals are systems that spontaneously break time-translation symmetry, exhibiting repeating patterns in time. Recent work has shown that non-Hermitian Floquet systems can host a time crystalline phase with quasi-long-range order. In…

Strongly Correlated Electrons · Physics 2025-03-31 Weihua Xie , Michael Kolodrubetz , Vadim Oganesyan , Daniel P. Arovas

Discrete time crystals are novel phases of matter that break the discrete time translational symmetry of a periodically driven system. In this work, we propose a classical system of weakly-nonlinear parametrically-driven coupled oscillators…

Statistical Mechanics · Physics 2025-01-31 Stuart Yi-Thomas , Jay D. Sau

Floquet (periodically driven) systems can give rise to unique non-equilibrium phases of matter without equilibrium analogs. The most prominent example is the realization of discrete time crystals. An intriguing question emerges: what other…

This paper investigates the possibility of generating Floquet-time crystals in higher dimensions ($d\geq 2$) through the time-periodic driving of integrable free-fermionic models. The realization leads to rigid time-crystal phases that are…

Strongly Correlated Electrons · Physics 2024-05-13 Rahul Chandra , Analabha Roy

Continuous time crystals (CTCs) - media with broken continuous time translation symmetry - are an eagerly sought state of matter that spontaneously transition from a time-independent state to one of periodic motion in response to a small…

We introduce a boundary condition twisted by time translation as a novel probe to characterize dynamical phases in periodically driven (Floquet) quantum systems. Inspired by twisted boundary conditions in equilibrium systems, this approach…

Statistical Mechanics · Physics 2025-11-17 Ryota Nakai , Taozhi Guo , Shinsei Ryu

Boundary time crystals (BTC's) are non-equilibrium phases of matter occurring in quantum systems in contact to an environment, for which a macroscopic fraction of the many body system breaks time translation symmetry. We study BTC's in…

Statistical Mechanics · Physics 2021-05-24 Luis Fernando dos Prazeres , Leonardo da Silva Souza , Fernando Iemini

We consider a dissipative quantum Ising model periodically driven by a train of $\pi$-pulses and investigate dissipative discrete time crystals (DTCs) in solids. In this model, the interaction between the spins spontaneously breaks the…

Statistical Mechanics · Physics 2022-06-01 Koki Chinzei , Tatsuhiko N. Ikeda
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