Absence of temporal order in states with spatial correlation decay
arXiv:1912.01210
Abstract
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. Assuming translational invariance, we obtain a similar bound on the temporal order between local operators at late times. Our proofs do not require any locality of the Hamiltonian. Applications in quantum time crystals are briefly discussed.
arXiv commentv2: very minor extension of the results in v1
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