# Absence of temporal order in states with spatial correlation decay

@article{Huang2019AbsenceOT, title={Absence of temporal order in states with spatial correlation decay}, author={Yichen Huang}, journal={arXiv: Statistical Mechanics}, year={2019} }

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.

## One Citation

Reply to "Comment on "Quantum Time Crystals from Hamiltonians with Long-Range Interactions""

- Physics
- 2020

In the note by Khemani et al. [arXiv:2001.11037] the authors express conceptual disagreement with our recent paper on quantum time crystals [Phys. Rev. Lett. 123, 210602]. They criticise the…

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