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 timedependent correlation functions of the order parameter. We then prove a nogo 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 nottoolongrange interactions.
 Publication:

Physical Review Letters
 Pub Date:
 June 2015
 DOI:
 10.1103/PhysRevLett.114.251603
 arXiv:
 arXiv:1410.2143
 Bibcode:
 2015PhRvL.114y1603W
 Keywords:

 11.30.j;
 05.70.Ln;
 73.22.Gk;
 Symmetry and conservation laws;
 Nonequilibrium and irreversible thermodynamics;
 Broken symmetry phases;
 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Other Condensed Matter;
 High Energy Physics  Theory;
 Mathematical Physics;
 Quantum Physics
 EPrint:
 5 pages, 1 figure