Langevin Simulation of the Chirally Decomposed Sine-Gordon Model

TL;DR

This paper develops a stable Langevin simulation method for the chirally decomposed sine-Gordon model, a complex action field theory, demonstrating the preservation of critical behavior and phase transitions.

Contribution

It introduces a truncation scheme in Langevin equations that stabilizes simulations without losing the model's critical properties.

Findings

Finite size scaling confirms the phase transition behavior.

The truncated Langevin approach maintains the Berezinskii-Kosterlitz-Thouless transition.

Numerical stability is achieved in simulations of complex action models.

Abstract

A large class of quantum and statistical field theoretical models, encompassing relevant condensed matter and non-abelian gauge systems, are defined in terms of complex actions. As the ordinary Monte-Carlo methods are useless in dealing with these models, alternative computational strategies have been proposed along the years. The Langevin technique, in particular, is known to be frequently plagued with difficulties such as strong numerical instabilities or subtle ergodic behavior. Regarding the chirally decomposed version of the sine-Gordon model as a prototypical case for the failure of the Langevin approach, we devise a truncation prescription in the stochastic differential equations which yields numerical stability and is assumed not to spoil the Berezinskii-Kosterlitz-Thouless transition. This conjecture is supported by a finite size scaling analysis, whereby a massive phase ending at a line of critical points is clearly observed for the truncated stochastic model.