# Classical discrete time crystals

@article{Yao2020ClassicalDT, title={Classical discrete time crystals}, author={Norman Y. Yao and C. Nayak and Leon Balents and Michael P. Zaletel}, journal={Nature Physics}, year={2020}, volume={16}, pages={438-447} }

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 subharmonic oscillations that depend upon an interplay of non-equilibrium driving, many-body interactions and the breakdown of ergodicity. However, subharmonic responses are also a well-known feature of classical dynamical systems ranging from predator–prey models to Faraday waves and a.c.-driven charge…

## 70 Citations

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…

The role of fluctuations in quantum and classical time crystals

- Physics
- 2022

Discrete time crystals (DTCs) are a many-body state of matter whose dynamics are slower than the forces acting on it. The same is true for classical systems with period-doubling bifurcations. Hence,…

Thermal melting of discrete time crystals: A dynamical phase transition induced by thermal fluctuations

- PhysicsPhysical Review B
- 2022

The stability of a discrete time crystal against thermal fluctuations has been studied numerically by solving a stochastic Landau-Lifshitz-Gilbert equation of a periodically-driven classical system…

Anharmonic classical time crystals: A coresonance pattern formation mechanism

- Physics
- 2021

Driven many-body systems have been shown to exhibit discrete time crystal phases characterized by broken discrete time-translational symmetry. This has been achieved generally through a subharmonic…

A Brief History of Time Crystals.

- Physics
- 2019

The idea of breaking time-translation symmetry has fascinated humanity at least since ancient proposals of the perpetuum mobile. Unlike the breaking of other symmetries, such as spatial translation…

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.

Classical Prethermal Phases of Matter.

- PhysicsPhysical review letters
- 2021

Studying the Hamiltonian dynamics of a large three-dimensional lattice of classical spins, this work provides the first numerical proof of prethermal phases of matter in a system with short-range interactions.

Floquet Phases of Matter via Classical Prethermalization.

- PhysicsPhysical review letters
- 2021

It is demonstrated that the prethermal regime of periodically driven (Floquet), classical many-body systems can host nonequilibrium phases of matter and it is proved that the effective Hamiltonian can host emergent symmetries protected by the discrete time-translation symmetry of the drive.

Supplemental Material for Classical many-body time crystals

- Physics
- 2019

Discrete time crystals are a many-body state of matter where the extensive system’s dynamics are slower than the forces acting on it. Nowadays, there is a growing debate regarding the specific…

Many-body–localized discrete time crystal with a programmable spin-based quantum simulator

- PhysicsScience
- 2021

The results are consistent with the realization of an out-of-equilibrium Floquet phase of matter and introduce a programmable quantum simulator based on solid-state spins for exploring many-body physics.

## References

SHOWING 1-10 OF 163 REFERENCES

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.

Observation of discrete time-crystalline order in a disordered dipolar many-body system

- PhysicsNature
- 2017

This work observes long-lived temporal correlations, experimentally identifies the phase boundary and finds that the temporal order is protected by strong interactions, which opens the door to exploring dynamical phases of matter and controlling interacting, disordered many-body 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.

Discrete Time Crystals

- Physics
- 2019

Experimental advances have allowed for the exploration of nearly isolated quantum many-body systems whose coupling to an external bath is very weak. A particularly interesting class of such systems…

Pre-thermal phases of matter protected by time-translation symmetry

- Mathematics
- 2016

In a periodically driven (Floquet) system, there is the possibility for new phases of matter, not present in stationary systems, protected by discrete time-translation symmetry. This includes…

Fate of a discrete time crystal in an open system

- Physics
- 2017

Following the recent realisation that periodically driven quantum matter can support new types of spatiotemporal order, now known as discrete time crystals (DTCs), we consider the stability of this…

Nonequilibrium first-order phase transition in coupled oscillator systems with inertia and noise.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2014

It is demonstrated that the dynamics of a system of coupled oscillators of distributed natural frequencies undergoes a nonequilibrium first-order phase transition from a synchronized phase at low parameter values to an incoherent phase at high values, and the escape time out of metastable states scales exponentially with the number of oscillators.

Absolute stability and spatiotemporal long-range order in Floquet systems

- Physics
- 2016

Recent work has shown that a variety of novel phases of matter arise in periodically driven Floquet systems. Among these are many-body localized phases which spontaneously break global symmetries and…

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.

Stability and pre-thermalization in chains of classical kicked rotors

- PhysicsJournal of Physics A: Mathematical and Theoretical
- 2018

Periodic drives are a common tool to control physical systems, but have a limited applicability because time-dependent drives generically lead to heating. How to prevent the heating is a fundamental…