  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.
