title: Absence of Quantum Time Crystals.
abstract: 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.
authors.affiliation: Department of Physics, University of California, Berkeley, California 94720, USA.
authors.forename: Haruki
authors.initials: H
authors.lastname: Watanabe
authors.affiliation: Institute for Solid State Physics, University of Tokyo, Kashiwa 277-8581, Japan.
authors.forename: Masaki
authors.initials: M
authors.lastname: Oshikawa