Thirring model at finite density in 0+1 dimensions with stochastic quantization: Crosscheck with an exact solution

TL;DR

This paper examines the effectiveness of stochastic quantization via complex Langevin evolution in solving the sign problem in a 0+1 dimensional Thirring model at finite density, validated against exact solutions.

Contribution

It provides a detailed analysis of the convergence and applicability of complex Langevin methods for this model, supported by analytical and numerical comparisons.

Findings

Complex Langevin can accurately solve the model in certain parameter regions.

Analytical results confirm numerical convergence properties.

Indirect indicators help assess correctness of stochastic quantization.

Abstract

We consider a generalized Thirring model in 0+1 dimensions at finite density. In order to deal with the resulting sign problem we employ stochastic quantization, i.e., a complex Langevin evolution. We investigate the convergence properties of this approach and check in which parameter regions complex Langevin evolutions are applicable in this setting. To this end we derive numerous analytical results and compare directly with numerical results. In addition we employ indirect indicators to check for correctness. Finally we interpret and discuss our findings.