Slowly decaying real-time oscillations in instanton crystal

Instanton crystal is a fascinating phase which is encountered when the minimum of the free energy corresponds to a configuration with an imaginary-time-dependent order parameter in the form of a chain of alternating instantons and anti-instantons. We present the results of the investigation of the real-time correlation functions of the order parameter in the instanton crystal phase. In order to obtain the correlation functions in real-time, we formulate an original method of analytic continuation from imaginary times, which is easily adapted into an efficient numerical scheme for the computations. The resulting correlation functions exhibit non-trivial slowly decaying oscillations in real-time, which is reminiscent of prethermal time crystals.