# Discrete Time Crystals: Rigidity, Criticality, and Realizations.

@article{Yao2016DiscreteTC, title={Discrete Time Crystals: Rigidity, Criticality, and Realizations.}, author={Norman Y. Yao and Andrew C. Potter and Ionut-Dragos Potirniche and Ashvin Vishwanath}, journal={Physical review letters}, year={2016}, volume={118 3}, pages={ 030401 } }

Despite being forbidden in equilibrium, spontaneous breaking of time translation symmetry can occur in periodically driven, Floquet systems with discrete time-translation symmetry. The period of the resulting discrete time crystal is quantized to an integer multiple of the drive period, arising from a combination of collective synchronization and many body localization. Here, we consider a simple model for a one-dimensional discrete time crystal which explicitly reveals the rigidity of the…

## 325 Citations

### Classical discrete time crystals

- PhysicsNature Physics
- 2020

The spontaneous breaking of time-translation symmetry in periodically driven quantum systems leads to a new phase of matter: the discrete time crystal (DTC). This phase exhibits collective…

### Time crystals: Analysis of experimental conditions

- PhysicsPhysical Review A
- 2018

Time crystals are quantum many-body systems which are able to self-organize their motion in a periodic way in time. Discrete time crystals have been experimentally demonstrated in spin systems.…

### Observation of a discrete time crystal

- PhysicsNature
- 2017

The experimental observation of a discrete time crystal, in an interacting spin chain of trapped atomic ions, is presented, which opens the door to the study of systems with long-range spatio-temporal correlations and novel phases of matter that emerge under intrinsically non-equilibrium conditions.

### Time-crystalline behavior in an engineered spin chain

- PhysicsPhysical Review B
- 2019

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…

### Clean Floquet Time Crystals: Models and Realizations in Cold Atoms.

- PhysicsPhysical review letters
- 2018

It is pointed out that time crystals can generally exist in systems without disorder, and a series of clean quasi-one-dimensional models under Floquet driving are proposed to demonstrate this unexpected result in principle.

### Time-crystalline phases and period-doubling oscillations in one-dimensional Floquet topological insulators

- Physics
- 2020

In this work, we reported a ubiquitous presence of topological Floquet time crystal (TFTC) in one-dimensional periodically-driven systems. The rigidity and realization of spontaneous discrete…

### Dissipative discrete time crystals

- Physics
- 2018

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…

### Building Continuous Time Crystals from Rare Events.

- PhysicsPhysical review letters
- 2020

Using Doob's transform as a tool, this work provides a mechanism to build classical time-crystal generators from the rare event statistics of some driven diffusive systems and uncovers striking similarities, but also key differences, with the Kuramoto synchronization transition.

### Route to Extend the Lifetime of a Discrete Time Crystal in a Finite Spin Chain without Disorder

- Physics
- 2021

Periodically driven (Floquet) systems are described by time-dependent Hamiltonians that possess discrete time translation symmetry. The spontaneous breaking of this symmetry leads to the emergence of…

### Criticality and rigidity of dissipative discrete time crystals in solids

- PhysicsPhysical Review Research
- 2022

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

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