# Boundary Time Crystals.

@article{Iemini2017BoundaryTC, title={Boundary Time Crystals.}, author={Fernando Iemini and Angelo Russomanno and Jonathan Keeling and Marco Schir{\`o} and Marcello Dalmonte and Rosario Fazio}, journal={Physical review letters}, year={2017}, volume={121 3}, pages={ 035301 } }

In this work we introduce boundary time crystals. Here continuous time-translation symmetry breaking occurs only in a macroscopic fraction of a many-body quantum system. After introducing their definition and properties, we analyze in detail a solvable model where an accurate scaling analysis can be performed. The existence of the boundary time crystals is intimately connected to the emergence of a time-periodic steady state in the thermodynamic limit of a many-body open quantum system. We also…

## 117 Citations

### Discrete Time Crystals in the Absence of Manifest Symmetries or Disorder in Open Quantum Systems.

- PhysicsPhysical review letters
- 2019

A semiclassical approach reveals the emergence of a robust discrete time-crystalline phase in the thermodynamic limit in which metastability, dissipation, and interparticle interactions play a crucial role.

### Exact solution of a boundary time-crystal phase transition: Time-translation symmetry breaking and non-Markovian dynamics of correlations

- PhysicsPhysical Review A
- 2022

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…

### Imaginary Time Crystal of Thermal Quantum Matter

- PhysicsChinese Physics Letters
- 2020

Spontaneous symmetry breaking is responsible for rich quantum phenomena from crystalline structures to superconductivity. This concept was boldly extended to the breaking of time translation, opening…

### Dynamical quantum phase transitions in systems with broken continuous time and space translation symmetries

- PhysicsPhysical Review A
- 2018

Spontaneous breaking of continuous time translation symmetry into a discrete one is related to time crystal formation. While the phenomenon is not possible in the ground state of a time-independent…

### Classical Many-Body Time Crystals.

- Physics, Computer SciencePhysical review letters
- 2019

This work provides a simple and pedagogical framework by which to obtain many-body time crystals using parametrically coupled resonators and presents a clear distinction between single-mode time-translation symmetry breaking and a situation where an extensive number of degrees of freedom undergo the transition.

### Time crystallinity in open quantum systems

- PhysicsQuantum
- 2020

A way to identify an open system time crystal based on a single object: the Floquet propagator is proposed and time-crystalline behavior in an explicitly short-range interacting open system is shown and the crucial role of the nature of the decay processes is demonstrated.

### A dissipative time crystal with or without Z2 symmetry breaking

- PhysicsNew Journal of Physics
- 2020

We study an emergent semiclassical time crystal composed of two interacting driven-dissipative bosonic modes. The system has a discrete Z2 spatial symmetry which, depending on the strength of the…

### Fractional time crystals

- PhysicsPhysical Review A
- 2019

Time crystals are quantum systems that are able to reveal condensed matter behavior in the time domain. It is known that crystallization in time can be observed in a periodically driven many-body…

### Isolated Heisenberg magnet as a quantum time crystal

- PhysicsPhysical Review B
- 2020

Local observables of closed many-body quantum systems are generally believed to quickly equilibrate after a quench, according to the eigenstate thermalization hypothesis. Here, the authors show that…

### Time crystals: a review

- PhysicsReports on progress in physics. Physical Society
- 2018

The struggle to observe discrete time crystals is reviewed here together with propositions that generalize this concept introducing condensed matter like physics in the time domain.

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