Can stochastic quantization evade the sign problem? -- the relativistic Bose gas at finite chemical potential

TL;DR

This paper investigates whether stochastic quantization can overcome the sign problem in complex action field theories, using the relativistic Bose gas at finite chemical potential as a test case, and finds promising results.

Contribution

The study demonstrates that stochastic quantization effectively handles the sign problem in the relativistic Bose gas at finite chemical potential, suggesting potential for QCD at nonzero density.

Findings

Sign problem is severe but manageable with stochastic quantization.

Chemical potential independence observed at small values.

Transition to a condensed phase at large chemical potential.

Abstract

A nonperturbative study of field theories with a complex action, such as QCD at finite baryon density, is difficult due to the sign problem. We show that the relativistic Bose gas at finite chemical potential has a sign and `Silver Blaze' problem, similar to QCD. We then apply stochastic quantization and complex Langevin dynamics to study this theory with nonperturbative lattice simulations. Independence of chemical potential at small and a transition to a condensed phase at large chemical potential are found. Lattices of size N^4, with N=4,6,8,10, are used. We show that the sign problem is severe, however, we find that it has no negative effect using this approach. This improves the prospects of applying stochastic quantization to QCD at nonzero density.