Controlling complex Langevin dynamics at finite density

TL;DR

This paper reviews the complex Langevin method for simulating finite density lattice field theories, discusses gauge cooling techniques to control its stability, and presents new results in related models and QCD.

Contribution

It introduces and evaluates gauge cooling methods for complex Langevin dynamics in nonabelian gauge theories, enhancing the method's reliability.

Findings

Gauge cooling improves stability of complex Langevin simulations.

New results in Polyakov chain models and heavy quark QCD.

Comparison of adaptive cooling implementations.

Abstract

At nonzero chemical potential the numerical sign problem in lattice field theory limits the use of standard algorithms based on importance sampling. Complex Langevin dynamics provides a possible solution, but it has to be applied with care. In this review, we first summarise our current understanding of the approach, combining analytical and numerical insight. In the second part we study SL(N,C) gauge cooling, which was introduced recently as a tool to control complex Langevin dynamics in nonabelian gauge theories. We present new results in Polyakov chain models and in QCD with heavy quarks and compare various adaptive cooling implementations.