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Many-body quantum systems, under suitable conditions, exhibit time-translation symmetry breaking and settle in a discrete time crystalline (DTC) phase -- an out-of-equilibrium quantum phase of matter. The defining feature of DTC is a robust…

Quantum Physics · Physics 2025-11-14 Gourab Das , Saptarshi Saha , Rangeet Bhattacharyya

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

Continuous time crystals (CTCs) are characterized by sustained oscillations that break the time translation symmetry. Since the ruling out of equilibrium CTCs by no-go theorems, the emergence of such dynamical phases has been observed in…

Quantum Physics · Physics 2024-05-01 Ya-Xin Xiang , Qun-Li Lei , Zhengyang Bai , Yu-Qiang Ma

We study Boundary time crystals (BTCs) in the presence of non-Markovian dynamics. In contrast to BTCs observed in earlier works in the Markovian regime, we show that non-Markovian dynamics can be highly beneficial for stabilizing BTCs over…

Quantum Physics · Physics 2026-05-08 Bandita Das , Rahul Ghosh , Victor Mukherjee

Here we provide a theoretical framework to analyze discrete time-crystalline phases (DTC) in open quantum many-body systems. As a particular realization, we choose a quantum many-body system that exhibits cascaded prethermalization . The…

Quantum Physics · Physics 2023-09-01 Saptarshi Saha , Rangeet Bhattacharyya

In this work we study genuine multipartite correlations (GMC's) in a boundary time crystal (BTC). Boundary time crystals are nonequilibrium quantum phases of matter in contact to an environment, for which a macroscopic fraction of the…

Quantum synchronization (QS) in dissipative systems is often inferred from smooth phase locking, leaving open whether its breakdown constitutes a genuine nonequilibrium transition. Here we introduce a Liouvillian framework that classifies…

Quantum Physics · Physics 2026-03-17 Jun Wang , Shu Yang , Zeqing Wang , Ran Qi , Haiping Hu , Weidong Li , Jianwen Jie

The spontaneous breaking of time-translation symmetry in periodically driven quantum systems leads to a new phase of matter: discrete time crystals (DTC). This phase exhibits collective subharmonic oscillations that depend upon an interplay…

Statistical Mechanics · Physics 2020-04-21 Norman Y. Yao , Chetan Nayak , Leon Balents , Michael P. Zaletel

Boundary time crystals are a class of exotic dissipative quantum phases that spontaneously break continuous time-translation symmetry in the thermodynamic limit of open quantum systems. In finite-size systems, the long-time evolution of…

Quantum Physics · Physics 2025-10-06 Zeping Liu , Yaotian Li , Zhaoyu Fei , Xiaoguang Wang

Periodically driven quantum systems host a range of non-equilibrium phenomena which are unrealizable at equilibrium. Discrete time-translational symmetry in a periodically driven many-body system can be spontaneously broken to form a…

Mesoscale and Nanoscale Physics · Physics 2019-06-11 James O'Sullivan , Oliver Lunt , Christoph W. Zollitsch , M. L. W. Thewalt , John J. L. Morton , Arijeet Pal

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

The breaking of the continuous time-translation symmetry manifests, in Markovian open quantum systems, through the emergence of non-stationary dynamical phases. Systems that display nonequilibrium transitions into these phases are referred…

Statistical Mechanics · Physics 2022-05-04 Federico Carollo , Igor Lesanovsky

Boundary time crystals (BTCs) in dissipative collective spin systems have been extensively studied using numerical, mean-field, and perturbative approaches. However, an explicit Liouvillian description governing the long-time dynamics deep…

Quantum Physics · Physics 2026-02-20 Dominik Nemeth , Alessandro Principi , Ahsan Nazir

Recent experiments with dense laser-driven atomic gases [G. Ferioli et al., arXiv:2207.10361 (2022)] have realized a many-body system which in the thermodynamic limit yields a so-called boundary time-crystal. This state of matter is…

Quantum Physics · Physics 2023-10-19 Albert Cabot , Leah Sophie Muhle , Federico Carollo , Igor Lesanovsky

We demonstrate the existence of a dynamical quantum phase transition (DQPT) in a dissipative collective-spin model that exhibits the boundary time crystal (BTC) phase. We initialize the system in the ground state of the Hamiltonian in…

Quantum Physics · Physics 2026-02-05 Sukrut Mondkar , Priya Ghosh , Ujjwal Sen

Discrete (DTCs) and continuous time crystals (CTCs) are novel dynamical many-body states, that are characterized by robust self-sustained oscillations, emerging via spontaneous breaking of discrete or continuous time translation symmetry.…

Boundary time crystals exhibit spontaneous breaking of continuous time-translation symmetry through persistent periodic oscillations in driven-dissipative many-body systems. Here, we show that multilevel interference provides a natural…

Quantum Physics · Physics 2026-05-27 Kang Shen , Xiangming Hu , Fei Wang

Boundary time crystals (BTCs) break time-translation symmetry and exhibit long-lived, robust oscillations insensitive to initial conditions. We show that collective spin BTCs can admit emergent topological winding numbers in operator space.…

Quantum Physics · Physics 2026-02-23 Dominik Nemeth , Ahsan Nazir , Alessandro Principi , Robert-Jan Slager

Discrete time crystals (DTCs) are new phases of matter characterized by the presence of an observable evolving with $nT$ periodicity under a $T$-periodic Hamiltonian, where $n>1$ is an integer insensitive to small parameter variations. In…

Quantum Physics · Physics 2020-01-17 Pekik Nurwantoro , Raditya Weda Bomantara , Jiangbin Gong

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…

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