Stochastic quantization at finite chemical potential

TL;DR

This paper explores stochastic quantization and complex Langevin dynamics to address the sign problem in lattice QCD at finite chemical potential, demonstrating promising results in simplified models and partial understanding of underlying mechanisms.

Contribution

It applies stochastic quantization to finite chemical potential QCD, providing new insights and validating the method against exact results in simplified models.

Findings

Excellent agreement with exact results in models with severe sign problem

Detailed analysis of the phase of the determinant and classical flow diagrams

Partial understanding of the Fokker-Planck eigenvalues in this context

Abstract

A nonperturbative lattice study of QCD at finite chemical potential is complicated due to the complex fermion determinant and the sign problem. Here we apply the method of stochastic quantization and complex Langevin dynamics to this problem. We present results for U(1) and SU(3) one link models and QCD at finite chemical potential using the hopping expansion. The phase of the determinant is studied in detail. Even in the region where the sign problem is severe, we find excellent agreement between the Langevin results and exact expressions, if available. We give a partial understanding of this in terms of classical flow diagrams and eigenvalues of the Fokker-Planck equation.