Complex Langevin Simulations of QCD at Finite Density -- Progress Report

TL;DR

This paper reports on progress in simulating finite-density QCD using the complex Langevin equation, focusing on testing its reliability and exploring conditions under which it produces accurate results.

Contribution

The study advances the application of complex Langevin simulations to finite-density QCD, including testing, identifying limitations, and exploring modifications for improved accuracy.

Findings

Simulations at certain parameters reproduce expected phase structures.

Current methods show limitations and fail in detailed results.

Moving to weaker couplings may improve reliability or reveal phase-quenched results.

Abstract

We simulate lattice QCD at finite quark-number chemical potential to study nuclear matter, using the complex Langevin equation (CLE). The CLE is used because the fermion determinant is complex so that standard methods relying on importance sampling fail. Adaptive methods and gauge-cooling are used to prevent runaway solutions. Even then, the CLE is not guaranteed to give correct results. We are therefore performing extensive testing to determine under what, if any, conditions we can achieve reliable results. Our earlier simulations at $\beta=6/g^2=5.6$, $m=0.025$ on a $12^4$ lattice reproduced the expected phase structure but failed in the details. Our current simulations at $\beta=5.7$ on a $16^4$ lattice fail in similar ways while showing some improvement. We are therefore moving to even weaker couplings to see if the CLE might produce the correct results in the continuum (weak-coupling) limit, or, if it still fails, whether it might reproduce the results of the phase-quenched theory. We also discuss action (and other dynamics) modifications which might improve the performance of the CLE.