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. An important feature of this phase is that the average of the order parameter over the imaginary time vanishes .
We propose a model that hosts the Instanton Crystal phase. The stability of the phase is proved both numerically and analytically in the certain region of parameters .
After that, 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 oscillations in real-time.
 G.A. Starkov and K.B. Efetov, Phys. Rev. B, 103, 075121 (2021)
 G.A. Starkov and K.B. Efetov, arXiv:2111.02346