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Discrete time crystals (DTCs) are emergent non-equilibrium phases of periodically driven many-body systems, with potential applications ranging from quantum computing to sensing and metrology. There has been significant recent interest in…

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

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

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 non-equilibrium phases of matter that break the discrete time-translation symmetry and is characterized by a robust subharmonic response in periodically driven quantum systems. Here, we explore the DTC in a…

Quantum Physics · Physics 2026-05-08 Ling-Zhi Tang , Xiao Li , Z. D. Wang , Dan-Wei Zhang

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

A discrete time crystal is a phase unique to nonequilibrium systems, where discrete time translation symmetry is spontaneously broken. Most of conventional time crystals proposed so far rely on spontaneous breaking of on-site symmetries and…

Mesoscale and Nanoscale Physics · Physics 2018-08-30 Kaoru Mizuta , Kazuaki Takasan , Masaya Nakagawa , Norio Kawakami

Discrete time crystal (DTC) has recently attracted increasing attention, but most DTC models and their properties are only revealed after disorder average. In this Letter, we propose a simple disorder-free periodically driven model that…

Strongly Correlated Electrons · Physics 2023-03-29 Shuo Liu , Shi-Xin Zhang , Chang-Yu Hsieh , Shengyu Zhang , Hong Yao

We characterize various dynamical phases of the simplest version of the quantum kicked top model, a paradigmatic system for studying quantum chaos, which exhibits both regular and chaotic behavior depending on the kick strength. In a…

Quantum Physics · Physics 2026-05-26 Subhashis Das , Vishal Khan , Atanu Rajak

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…

Discrete time crystals (DTC) have emerged as a significant phase of matter for out-of-equilibrium many-body systems. We study how long-range interactions and disorder contribute to the stability of the DTC phase. Generally, a stable DTC…

Disordered Systems and Neural Networks · Physics 2025-05-20 Aarya Bothra , Arti Garg

Discrete time crystals (DTC) have been demonstrated experimentally in several different quantum systems in the past few years. Spin couplings and cavity losses have been shown to play crucial roles for realizing DTC order in open many-body…

Quantum Physics · Physics 2022-02-03 Zhengda Hu , Xingyu Gao , Tongcang Li

We analyze the quantum dynamics of periodically driven, disordered systems in the presence of long-range interactions. Focusing on the stability of discrete time crystalline (DTC) order in such systems, we use a perturbative procedure to…

Disordered Systems and Neural Networks · Physics 2017-07-10 Wen Wei Ho , Soonwon Choi , Mikhail D. Lukin , Dmitry A. Abanin

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

Symmetries are well known to have had a profound role in our understanding of nature and are a critical design concept for the realization of advanced technologies. In fact, many symmetry-broken states associated with different phases of…

Quantum Physics · Physics 2021-04-01 A. Sakurai , V. M. Bastidas , W. J. Munro , Kae Nemoto

Our understanding of phases of matter relies on symmetry breaking, one example being water ice whose crystalline structure breaks the continuous translation symmetry of space. Recently, breaking of time translation symmetry was observed in…

We introduce a qudit-native framework for engineering rich and robust discrete time crystals (DTCs) by leveraging their internal multilevel structure. Unlike in qubit systems, qudit-based DTCs exhibit distinct dynamical mechanisms that…

Quantum Physics · Physics 2026-05-18 Wei-Guo Ma , Heng Fan , Shi-Xin Zhang

A quantum phase of matter can be understood from the symmetry of the system's Hamiltonian. The system symmetry along the time axis has been proposed to show a new phase of matter referred as discrete-time crystals (DTCs). A DTC is a quantum…

Quantum Physics · Physics 2021-08-25 Akitada Sakurai , Victor M. Bastidas , Marta P. Estarellas , William J. Munro , Kae Nemoto

The rich dynamics and phase structure of driven systems includes the recently described phenomenon of the "discrete time crystal" (DTC), a robust phase which spontaneously breaks the discrete time translation symmetry of its driving…

Quantum Physics · Physics 2018-05-18 Jared Rovny , Robert L. Blum , Sean E. Barrett

We demonstrate the realization of a Discrete Time-Crystal (DTC) phase in a family of periodically driven, one-dimensional quadratic lattice Hamiltonians that can be obtained using spin chains. These interactions preserve integrability while…

Strongly Correlated Electrons · Physics 2026-04-21 Rahul Chandra , Mahbub Rahaman , Soumyabroto Majumder , Analabha Roy , Sujit Sarkar