# Boundary Time Crystals.

@article{Iemini2018BoundaryTC, 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={2018}, 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…

## 113 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.

## References

SHOWING 1-10 OF 57 REFERENCES

### Defining time crystals via representation theory

- Physics
- 2017

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…

### Floquet Time Crystals.

- PhysicsPhysical review letters
- 2016

This work defines what it means for time translation symmetry to be spontaneously broken in a quantum system and shows that this occurs in a large class of many-body localized driven systems with discrete time-translation symmetry.

### Absence of Quantum Time Crystals.

- PhysicsPhysical review letters
- 2015

A no-go theorem is proved that rules out the possibility of time crystals defined as such, in the ground state or in the canonical ensemble of a general Hamiltonian, which consists of not-too-long-range interactions.

### 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.

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

- PhysicsPhysical review letters
- 2017

A simple model for a one-dimensional discrete time crystal which explicitly reveals the rigidity of the emergent oscillations as the drive is varied is considered and a blueprint based upon a one dimensional chain of trapped ions is proposed.

### 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.

### Discrete Time-Crystalline Order in Cavity and Circuit QED Systems.

- PhysicsPhysical review letters
- 2018

A phenomenology of dissipative discrete time crystals is established by generalizing the Landau theory of phase transitions to Floquet open systems and finding clear signatures of a transient discrete time-crystalline behavior, which is absent in the isolated counterpart.

### 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.

### Phase Structure of Driven Quantum Systems.

- PhysicsPhysical review letters
- 2016

It is shown that their disordered Floquet many-body localized counterparts can exhibit distinct ordered phases delineated by sharp transitions, and these are analogs of equilibrium states with broken symmetries and topological order.

### Time Crystal Behavior of Excited Eigenstates.

- PhysicsPhysical review letters
- 2017

This work simulates the process of the spontaneous symmetry breaking due to measurements of particle positions and analyzes the lifetime of the resulting symmetry broken state.