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In quantum lattice systems, we prove that any stationary state with power-law (or even exponential) decay of spatial correlations has vanishing macroscopic temporal order in the thermodynamic limit.
Gibbs states of a one dimensional quantum lattice
H. Araki · 1969
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The finite group velocity of quantum spin systems
E. H. Lieb and D. W. Robinson · 1972
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Spectral gap and exponential decay of correlations
M. B. Hastings and T. Koma · 2006
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Lieb-robinson bounds and the exponential clustering theorem
B. Nachtergaele and R. Sims · 2006
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Locality of temperature
M. Kliesch, C. Gogolin, M. J. Kastoryano, A. Riera, and J. Eisert · 2014
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Stringy effects in scrambling
S. H. Shenker and D. Stanford · 2015
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Absence of quantum time crystals
H. Watanabe and M. Oshikawa · 2015
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A bound on chaos
J. Maldacena, S. H. Shenker, and D. Stanford · 2016
Cited alongside, same era.
Time crystals: a review
K. Sacha and J. Zakrzewski · 2017
Cited alongside, same era.
Time evolution of correlation functions in quantum many-body systems
A. M. Alhambra, J. Riddell, and L. P. García-Pintos · 2019
Cited alongside, same era.
D. V. Else, C. Monroe, C. Nayak, and N. Y. Yao · 2019
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Finite-size scaling of out-of-time-ordered correlators at late times
Y. Huang, F. G. S. L. Brandão, and Y.-L. Zhang · 2019
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A brief history of time crystals
V. Khemani, R. Moessner, and S. L. Sondhi · 2019
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Quantum time crystals from Hamiltonians with long-range interactions
V. K. Kozin and O. Kyriienko · 2019
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Proof of the absence of long-range temporal orders in Gibbs states
H. Watanabe, M. Oshikawa, and T. Koma · 2019
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