Mean-field thermodynamic quantum time-space crystal: spontaneous breaking of time-translation symmetry in a macroscopic fermion system

Understand

A model demonstrating existence of a thermodynamically stable quantum time-space crystal has been proposed and studied.

• This state is characterized by an order parameter periodic in both real and imaginary times.
• The average of the order parameter over phases of the oscillations vanishes but correlation functions of two or more order parameters show non-decaying oscillations.
• An alternative interpretation of the results is based on a concept of an operator order parameter introduced for this purpose.