Phase transition into Instanton Crystal

TL;DR

This paper introduces a new class of models that exhibit an instanton crystal phase characterized by a time-dependent order parameter forming a chain of instantons and antiinstantons, with a phase transition to a static order parameter state.

Contribution

The paper develops an efficient numerical scheme to study instanton crystal phases and analytically demonstrates their existence in certain limits.

Findings

Existence of instanton crystal phase confirmed.

Phase transition between instanton crystal and static order parameter states.

Numerical scheme effectively analyzes the model across parameter space.

Abstract

We propose a class of models exhibiting instanton crystal phase. In this phase, the minimum of the free energy corresponds to a configuration with an imaginary-time-dependent order parameter in a form of a chain of alternating instantons and antiinstantons. The resulting characteristic feature of this state is that the average of the order parameter over the imaginary time vanishes. In order to study the model in a broad region of parameters of the model quantitatively, and prove the existence of the instanton crystal phase, we develop an efficient numerical scheme, suitable for the exact treatment of the proposed models. In a certain limit, results demonstrating the existence of the instanton crystal phase are obtained also analytically. The numerical study of the model shows that there is a phase transition between the instanton crystal and the state with the imaginary-time-independent order parameter.