Thirring model at finite density in 2+1 dimensions with stochastic quantization

TL;DR

This paper explores using stochastic quantization and complex Langevin dynamics to study the 2+1 dimensional Thirring model at finite density, aiming to overcome the sign problem and evaluate observables across chemical potentials.

Contribution

It demonstrates the applicability of stochastic quantization and complex Langevin methods to the finite density Thirring model in 2+1 dimensions, including analytical and numerical comparisons.

Findings

Analytical results in the heavy dense limit match numerical simulations.

The method enables evaluation of observables at various chemical potentials.

Indicators are used to verify correct convergence of the complex Langevin evolution.

Abstract

We consider a generalization of the Thirring model in 2+1 dimensions at finite density. We employ stochastic quantization and check for the applicability in the finite density case to circumvent the sign problem. To this end we derive analytical results in the heavy dense limit and compare with numerical ones obtained from a complex Langevin evolution. Furthermore we make use of indirect indicators to check for incorrect convergence of the underlying complex Langevin evolution. The method allows the numerical evaluation of observables at arbitrary values of the chemical potential. We evaluate the results and compare to the (0+1)-dimensional case.