2014/10/31 by Haruki Watanabe, Masaki Oshikawa · 3 citations
Physics and Astronomy · Mathematics · #cond-mat.stat-mech #cond-mat.other #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1103/physrevlett.114.251603
published as Phys. Rev. Lett. 114, 251603 (2015) · 5 pages, 1 figure; v3: A typo is corrected; the version to appear in Phys. Rev. Lett
arxiv created 2015/06/18 · arxiv updated 2015/06/26
In analogy with crystalline solids around us, Wilczek recently proposed the idea of "time crystals" as phases that spontaneously break the continuous time translation into a discrete subgroup. The proposal stimulated further studies and vigorous debates whether it can be realized in a physical system. However, a precise definition of the time crystal is needed to resolve the issue. Here we first present a definition of time crystals based on the time-dependent correlation functions of the order parameter. We then prove a no-go theorem that rules out the possibility of time crystals defined as such, in the ground state or in the canonical ensemble of a general Hamiltonian, which consists of not-too-long-range interactions.