Proof of the absence of long-range temporal orders in Gibbs states

Abstract

We address the question whether time translation symmetry can be spontaneously broken in a quantum many-body system. One way of detecting such a symmetry breaking is to examine the time-dependence of a correlation function. If the large-distance behavior of the correlation function exhibits a nontrivial time-dependence in the thermodynamic limit, the system would develop a temporal long-range order, realizing a time crystal. In an earlier publication, we sketched a proof for the absence of such time dependence in the thermal equilibrium described by the Gibbs state [H. Watanabe and M. Oshikawa, Phys. Rev. Lett. 114, 251603 (2015)]. Here we present a complete proof and extend the argument to a more general class of stationary states than the Gibbs states.

8 pages, no figure; v3: published version

References in corpus (3)

• Absence of Quantum Time Crystals
• Spin transport in a one-dimensional anisotropic Heisenberg model
• Comment on "Quantum Time Crystals": a new paradigm or just another proposal of perpetuum mobile?

Cited by in corpus (4)

• Lack of a genuine time crystal in a chiral soliton model
• Can a bright soliton model reveal a genuine time crystal for a finite number of bosons?
• Absence of temporal order in states with spatial correlation decay
• Reply to "Comment on "Quantum Time Crystals from Hamiltonians with Long-Range Interactions""