# Comment on "Space-time crystals of trapped ions".

@article{Bruno2013CommentO, title={Comment on "Space-time crystals of trapped ions".}, author={Patrick Bruno}, journal={Physical review letters}, year={2013}, volume={111 2}, pages={ 029301 } }

A Comment on "Space-Time Crystals of Trapped ions", by Tongcang Li et al. (PRL 109, 163001 (2012); arXiv:1206.4772

## 37 Citations

### 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.

### 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.

### 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.

### Classical and quantum time crystals in a levitated nanoparticle without drive

- Physics
- 2020

Time crystal is defined as a phase of matter spontaneously exhibiting a periodicity in time. Previous studies focused on discrete quantum time crystals under periodic drive. Here, we propose a time…

### Quasi time crystal

- Physics
- 2022

We discuss the possibility of making a quasi time crystal. A simple two-state model is studied to clarify our definition. In a superposition of the ground state and the excited state and the…

### Order parameter in electron systems: its fluctuations and oscillations

- Physics
- 2019

The concept of the order parameter is extremely useful in physics. Here, I discuss extensions of this concept to cases when the order parameter is no longer a constant but ﬂuctuates or oscillates in…

### ORDER PARAMETER IN ELECTRON SYSTEMS: ITS FLUCTUATIONS AND OSCILLATIONS

- PhysicsЖУРНАЛ ЭКСПЕРИМЕНТАЛЬНОЙ И ТЕОРЕТИЧЕСКОЙ ФИЗИКИ
- 2019

The concept of the order parameter is extremely useful in physics. Here, I discuss extensions of this concept to cases when the order parameter is no longer a constant but fluctuates or oscillates in…

### 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…

### Trial wave functions for ring-trapped ions and neutral atoms: Microscopic description of the quantum space-time crystal

- Physics
- 2017

A constructive theoretical platform for the description of quantum space-time crystals uncovers for $N$ interacting and ring-confined rotating particles the existence of low-lying states with proper…

### 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…

## References

### Part 1, Gordon and Breach, 1970; for an elementary discussion, see J. van Wezel and J. van den Brink

- Lectures on Quantum Statistics
- 2007