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We address the question whether time translation symmetry can be spontaneously broken in a quantum many-body system.
V. Else D, C. Monroe, C. Nayak, and N. Y. Yao, “Discrete time crystals,” arXiv:1905.13232
1905
Earlier work this paper cites.
V. Khemani, R. Moessner, and S. L. Sondhi, “A brief history of time crystals,” arXiv:1910.10745
1910
Earlier work this paper cites.
1911
Earlier work this paper cites.
1912
Earlier work this paper cites.
Elliott H. Lieb and Derek W. Robinson, “The finite group velocity of quantum spin systems,” Commun. Math. Phys. 28
1972
Earlier work this paper cites.
Marko Žnidarič, “Spin transport in a one-dimensional anisotropic heisenberg model,” Phys. Rev. Lett. 106
2011
Earlier work this paper cites.
Frank Wilczek, “Quantum time crystals,” Phys. Rev. Lett. 109
2012
Cited alongside, same era.
Haruki Watanabe and Masaki Oshikawa, “Absence of quantum time crystals,” Phys. Rev. Lett. 114
2015
Cited alongside, same era.
Krzysztof Sacha, “Modeling spontaneous breaking of time-translation symmetry,” Phys. Rev. A 91
2015
Cited alongside, same era.
Vedika Khemani, Achilleas Lazarides, Roderich Moessner, and S. L. Sondhi, “Phase structure of driven quantum systems,” Phys. Rev. Lett. 116
2016
Cited alongside, same era.
Dominic V. Else, Bela Bauer, and Chetan Nayak, “Floquet time crystals,” Phys. Rev. Lett. 117
2016
Cited alongside, same era.
N. Y. Yao, A. C. Potter, I.-D. Potirniche, and A. Vishwanath, “Discrete time crystals: Rigidity, criticality, and realizations,” Phys. Rev. Lett. 118
Soonwon Choi, Joonhee Choi, Renate Landig, Georg Kucsko, Hengyun Zhou, Junichi Isoya, Fedor Jelezko, Shinobu Onoda, Hitoshi Sumiya, Vedika Khemani, Curt von Keyserlingk, Norman Y. Yao, Eugene Demler, and Mikhail D. Lukin, “Observation of discrete time-crystalline order in a disordered dipolar many-body system,” Nature 543
2017
Later among the works it cites.
J. Zhang, P. W. Hess, A. Kyprianidis, P. Becker, A. Lee, J. Smith, G. Pagano, I. D. Potirniche, A. C. Potter, A. Vishwanath, N. Y. Yao, and C. Monroe, “Observation of a discrete time crystal,” Nature 543
2017
Later among the works it cites.
Krzysztof Sacha and Jakub Zakrzewski, “Time crystals: a review,” Reports on Progress in Physics 81
2017
Later among the works it cites.
Andrzej Syrwid, Jakub Zakrzewski, and Krzysztof Sacha, “Time crystal behavior of excited eigenstates,” Phys. Rev. Lett. 119
2017
Later among the works it cites.
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2017
Cited alongside, same era.
P. Bruno, “Comment on “Quantum Time Crystals”,” Phys. Rev. Lett. 110
Cited in the paper.
Patrick Bruno, “Impossibility of spontaneously rotating time crystals: A no-go theorem,” Phys. Rev. Lett. 111
Cited in the paper.
M. B. Hastings, “Locality in quantum systems,” arXiv:1008.5137
Cited in the paper.
The operator norm of an operator \mathaccentV h a t 05 E O \mathaccentV{hat}05E{O} is defined as ∥ \mathaccentV h a t 05 E O ∥ := sup | ψ ⟩ , ∥ | ψ ⟩ | ∥ > 0 ∥ \mathaccentV h a t 05 E O | ψ ⟩ ∥ / ∥ | ψ ⟩ ∥ {\delimiter 2536205}\mathaccentV{hat}05E{O}{\delimiter 2536205}:=\text{sup}_{|\psi\delimiter 86414091,{\delimiter 2536205}{|\psi\delimiter 86414091}|{\delimiter 2536205}>0}{\delimiter 2536205}\mathaccentV{hat}05E{O}{|\psi\delimiter 86414091}{\delimiter 2536205}/{\delimiter 2536205}{|\psi\delimiter 86414091}{\delimiter 2536205}
Cited in the paper.
For the assumed boundedness, the maximum number of bosons that can occupy a single site must be a finite number independent of the system size
Cited in the paper.
An example of η + ( ω ) \eta^{+}(\omega) for the range ε ≤ ω ≤ 2 ε \varepsilon\leq\omega\leq 2\varepsilon and K ≤ ω ≤ K + ε K\leq\omega\leq K+\varepsilon can be constructed using m ( x ) := ∫ − 1 x d y e − 1 1 − y 2 m(x):=\intop\nolimits_{-1}^{x}dye^{-\frac{1}{1-y^{2}}} ( − 1 ≤ x ≤ + 1 -1\leq x\leq+1 ). For example, one can set η + ( ω ) = m ( 2 ω − 3 ε ε ) / m ( + 1 ) \eta^{+}(\omega)=m(\frac{2\omega-3\varepsilon}{\varepsilon})/m(+1) for ε ≤ ω ≤ 2 ε \varepsilon\leq\omega\leq 2\varepsilon
Cited in the paper.
Valerii K. Kozin and Oleksandr Kyriienko, “Quantum time crystals from Hamiltonians with long-range interactions,” Phys. Rev. Lett. 123
2019
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