Degenerate distributions in complex Langevin dynamics: one-dimensional QCD at finite chemical potential

TL;DR

This paper analytically shows that complex Langevin dynamics can accurately solve the sign problem in one-dimensional QCD at finite chemical potential by accounting for oscillating spectral densities and degenerate distributions.

Contribution

It reveals the existence of a continuum of degenerate distributions and classical fixed points that enable complex Langevin to correctly reproduce the chiral condensate.

Findings

Complex Langevin captures oscillating spectral density contributions.

Infinite classical fixed points exist in the thermodynamic limit.

Correct solutions arise from degenerate distributions in complex space.

Abstract

We demonstrate analytically that complex Langevin dynamics can solve the sign problem in one-dimensional QCD in the thermodynamic limit. In particular, it is shown that the contributions from the complex and highly oscillating spectral density of the Dirac operator to the chiral condensate are taken into account correctly. We find an infinite number of classical fixed points of the Langevin flow in the thermodynamic limit. The correct solution originates from a continuum of degenerate distributions in the complexified space.