Slowly decaying real-time oscillations in instanton crystal

TL;DR

This paper investigates real-time correlation functions in the instanton crystal phase, revealing slowly decaying oscillations that resemble prethermal time crystals, using a novel analytic continuation method.

Contribution

It introduces an original analytic continuation method to compute real-time correlations in the instanton crystal phase.

Findings

Correlation functions show slowly decaying oscillations in real-time.

The method is adaptable for efficient numerical computations.

Results suggest similarities to prethermal time crystals.

Abstract

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.