Complex Langevin in low-dimensional QCD: the good and the not-so-good

TL;DR

This paper investigates the complex Langevin method in low-dimensional QCD, showing it can produce correct results with gauge cooling in 1D but struggles in 2D under strong sign problems.

Contribution

It demonstrates the effectiveness and limitations of the complex Langevin method with gauge cooling in low-dimensional QCD.

Findings

Gauge cooling improves results in 1D QCD

Disagreement persists in 2D QCD with large sign problem

Method stability does not guarantee correctness

Abstract

We present our latest results on the application of the complex Langevin method to one- and two-dimensional QCD. Although the method is stable, it unfortunately converges to an incorrect result when applied as such. After applying additional gauge cooling steps, the results agree with the known analytical results in the one-dimensional case. However, in the two-dimensional case the disagreement subsists, even with gauge cooling, when the sign problem is sufficiently large.