# Impossibility of spontaneously rotating time crystals: a no-go theorem.

@article{Bruno2013ImpossibilityOS, title={Impossibility of spontaneously rotating time crystals: a no-go theorem.}, author={Patrick Bruno}, journal={Physical review letters}, year={2013}, volume={111 7}, pages={ 070402 } }

I present arguments indicating the impossibility of spontaneously rotating "quantum time crystals," as recently proposed by Frank Wilczek. In particular, I prove a "no-go theorem," rigorously ruling out the possibility of spontaneous ground-state (or thermal equilibrium) rotation for a broad class of systems.

## 136 Citations

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.

Condensed-matter physics: Marching to a different quantum beat

- PhysicsNature
- 2017

Two experiments have found evidence for a Floquet time crystal, which is characterized by persistent in‐phase oscillations, and this work aims to characterize this crystal as aperiodic oscillator.

Lack of a genuine time crystal in a chiral soliton model

- PhysicsPhysical Review Research
- 2020

In a recent publication [Phys. Rev. Lett. {\bf 124}, 178902] Ohberg and Wright claim that in a chiral soliton model it is possible to realize a genuine time crystal which corresponds to a periodic…

Existence of quantum time crystals

- Physics
- 2016

The existence of quantum time crystals is investigated and shown to be possible in pure phases defined by a state invariant under a group of space translations, as displayed by explicit examples.

Discrete time quasicrystals

- PhysicsPhysical Review B
- 2019

Periodically driven quantum many-body systems can spontaneously reorganize their motion and start moving with a period different than the driving period. These are ``discrete time crystals'' and they…

Boundary Time Crystals.

- PhysicsPhysical review letters
- 2018

This work introduces boundary time crystals and analyzes in detail a solvable model where an accurate scaling analysis can be performed.

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.

Mean-field thermodynamic quantum time-space crystal: Spontaneous breaking of time-translation symmetry in a macroscopic fermion system

- PhysicsPhysical Review B
- 2019

A model demonstrating existence of a thermodynamically stable quantum time-space crystal has been proposed and studied. This state is characterized by an order parameter periodic in both real and…

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…

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