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… 

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