Defining Time Crystals via Representation Theory
  Time crystals are proposed states of matter which spontaneously break time translation symmetry. There is no settled definition of such states. We offer a new definition which follows the traditional recipe for Wigner symmetries and order parameters. Supplementing our definition with a few plausible assumptions we find that a) systems with time independent Hamiltonians should not exhibit TTSB while b) the recently studied $\pi$ spin glass/Floquet time crystal can be viewed as breaking a global internal symmetry and as breaking time translation symmetry as befits its two names. 
Vedika Khemani, C. W. von Keyserlingk, S. L. Sondhi
cond-mat.stat-mech cond-mat.dis-nn hep-lat hep-th quant-ph