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.

5 pages, 1 figure; v3: A typo is corrected; the version to appear in Phys. Rev. Lett

References in corpus (3)

• Comment on "Quantum Time Crystals": a new paradigm or just another proposal of perpetuum mobile?
• Semiclassical time crystal in the chiral Gross-Neveu model
• On the dynamics of fluctuations in time crystals

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