# Quantum Time Crystals from Hamiltonians with Long-Range Interactions.

@article{Kozin2019QuantumTC, title={Quantum Time Crystals from Hamiltonians with Long-Range Interactions.}, author={Valerii K. Kozin and Oleksandr Kyriienko}, journal={Physical review letters}, year={2019}, volume={123 21}, pages={ 210602 } }

Time crystals correspond to a phase of matter where time-translational symmetry (TTS) is broken. Up to date, they are well studied in open quantum systems, where an external drive allows us to break discrete TTS, ultimately leading to Floquet time crystals. At the same time, genuine time crystals for closed quantum systems are believed to be impossible. In this study we propose a form of a Hamiltonian for which the unitary dynamics exhibits the time crystalline behavior and breaks continuous…

## 62 Citations

### Comment on "Quantum Time Crystals from Hamiltonians with Long-Range Interactions"

- Physics
- 2020

In a recent paper (Phys. Rev. Lett. 123, 210602), Kozin and Kyriienko claim to realize "genuine" ground state time crystals by studying models with long-ranged and infinite-body interactions. Here we…

### Discrete time crystals in Bose-Einstein condensates and the symmetry-breaking edge in a simple two-mode theory

- PhysicsPhysical Review A
- 2021

Discrete time crystals (DTCs) refer to a novel many-body steady state that spontaneously breaks the discrete time-translational symmetry in a periodically-driven quantum system. Here, we study DTCs…

### Discrete time crystals in many-body quantum chaos

- PhysicsPhysical Review B
- 2019

Discrete time crystals (DTCs) are new phases of matter characterized by the presence of an observable evolving with $nT$ periodicity under a $T$-periodic Hamiltonian, where $n>1$ is an integer…

### Quantum time crystals with programmable disorder in higher dimensions

- Physics
- 2020

We present fresh evidence for the presence of discrete quantum time crystals in two spatial dimensions. Discrete time crystals are intricate quantum systems that are concomitant with spontaneous…

### Discrete time crystal in the gradient-field Heisenberg model

- PhysicsPhysical Review B
- 2020

We show that time crystal phases, which are known to exist for disorder-based many-body localized systems, also appear in systems where localization is due to strong magnetic field gradients.…

### 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…

### Condensed matter physics in time crystals

- PhysicsNew Journal of Physics
- 2020

Time crystals are physical systems whose time translation symmetry is spontaneously broken. Although the spontaneous breaking of continuous time-translation symmetry in static systems is proved…

### Route to Extend the Lifetime of a Discrete Time Crystal in a Finite Spin Chain without Disorder

- Physics
- 2021

Periodically driven (Floquet) systems are described by time-dependent Hamiltonians that possess discrete time translation symmetry. The spontaneous breaking of this symmetry leads to the emergence of…

### Time Crystals Protected by Floquet Dynamical Symmetry in Hubbard Models.

- PhysicsPhysical review letters
- 2020

These time crystals arise only from the Floquet dynamical symmetry and thus appear in both dissipative and isolated systems and in the presence of disorder as long as the FDS is respected, and their experimental realizations in cold atom experiments are discussed.

### Reply to "Comment on "Quantum Time Crystals from Hamiltonians with Long-Range Interactions""

- Physics
- 2020

In the note by Khemani et al. [arXiv:2001.11037] the authors express conceptual disagreement with our recent paper on quantum time crystals [Phys. Rev. Lett. 123, 210602]. They criticise the…

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