Comment on "Quantum time crystals".

@article{Bruno2013CommentO,
  title={Comment on "Quantum time crystals".},
  author={Patrick Bruno},
  journal={Physical review letters},
  year={2013},
  volume={110 11},
  pages={
          118901
        }
}
  • P. Bruno
  • Published 15 October 2012
  • Physics, Medicine
  • Physical review letters
A Comment on Frank Wilczek's paper "Quantum Time Crystals" (Phys. Rev. Lett. 109, 160401 (2012); arXiv:1202.2539). 
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It is shown that the energy of the chiral soliton in the laboratory frame is not correctly calculated in the Letter and the correct energy becomes minimal if the soliton does not move.
Classes of metastable thermodynamic quantum time crystals
We found that thermodynamic quantum time crystals in fermi systems, defined as quantum orders oscillating periodically in the imaginary Matsubara time with zero mean, are metastable for two general
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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.
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Isolated Heisenberg magnet as a quantum time crystal
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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The concept of the modular energy operator is formalized within the Page and Wooters timeless framework and is elevated to the same status as the more studied modular operators of position and momentum.
Observation of a Space-Time Crystal in a Superfluid Quantum Gas.
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The observation of a space-time crystal using ultracold atoms, where the periodic structure in both space and time is directly visible in the experimental images, paving the way for the usage of space- time crystals for the discovery of novel nonequilibrium phases of matter.
Quantum Time Crystals from Hamiltonians with Long-Range Interactions.
TLDR
This study proposes a form of a Hamiltonian for which the unitary dynamics exhibits the time crystalline behavior and breaks continuous TTS, based on a spin-1/2 many-body Hamiltonian which has long-range multispin interactions in the form of spin strings, thus bypassing previously known no-go theorems.
Mean-field thermodynamic quantum time-space crystal: Spontaneous breaking of time-translation symmetry in a macroscopic fermion system
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
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