Absence of temporal order in states with spatial correlation decay
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.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2019
- DOI:
- 10.48550/arXiv.1912.01210
- arXiv:
- arXiv:1912.01210
- Bibcode:
- 2019arXiv191201210H
- Keywords:
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- Condensed Matter - Statistical Mechanics;
- Quantum Physics
- E-Print:
- v2: very minor extension of the results in v1