Time crystal behavior of excited eigenstates

Understand

In analogy to spontaneous breaking of continuous space translation symmetry in the process of space crystal formation, it was proposed that spontaneous breaking of continuous time translation symmetry could lead to time crystal formation.

• In other words, a time-independent system prepared in the energy ground state is expected to reveal periodic motion under infinitely weak perturbation.
• In the case of the system proposed originally by Frank Wilczek, spontaneous breaking of time translation symmetry can not be observed if one starts with the ground state.
• We point out that the symmetry breaking can take place if the system is prepared in an excited eigenstate.