Dynamical stabilisation of complex Langevin simulations of QCD

TL;DR

This paper introduces Dynamic Stabilisation (DS), a method to improve complex Langevin simulations of QCD by addressing instabilities, enabling more reliable exploration of QCD at finite density.

Contribution

The paper presents DS as a novel modification to complex Langevin dynamics, effectively stabilizing simulations of QCD with finite chemical potential.

Findings

DS successfully stabilizes complex Langevin simulations.

Application to heavy-dense QCD yields consistent results.

Enables exploration of QCD phase diagram at finite density.

Abstract

The ability to describe strongly interacting matter at finite temperature and baryon density provides the means to determine, for instance, the equation of state of QCD at non-zero baryon chemical potential. From a theoretical point of view, direct lattice simulations are hindered by the numerical sign problem, which prevents the use of traditional methods based on importance sampling. Despite recent successes, simulations using the complex Langevin method have been shown to exhibit instabilities, which cause convergence to wrong results. We introduce and discuss the method of Dynamic Stabilisation (DS), a modification of the complex Langevin process aimed at solving these instabilities. We present results of DS being applied to the heavy-dense approximation of QCD, as well as QCD with staggered fermions at zero chemical potential and finite chemical potential at high temperature. Our findings show that DS can successfully deal with the aforementioned instabilities, opening the way for further progress.