# 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…

## 50 Citations

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

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- 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

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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…

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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…

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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.…

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

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- 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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We address the question whether time translation symmetry can be spontaneously broken in a quantum many-body system. One way of detecting such a symmetry breaking is to examine the time-dependence of…

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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…

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It is speculated that systems with thermal phase transitions to multiple competing phases can give rise to DTCs when appropriately driven, and it is explicitly shown that the DTC is a genuine nonequilibrium state.

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It is demonstrated how the time crystalline qualities of a closed string are greatly enhanced when the string becomes knotted, which means that physical realizations of Hamiltonian time crystals can be constructed in terms of knotted ring molecules.

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