The Dirac spectrum in Complex Langevin Simulations of QCD

TL;DR

This paper demonstrates that in complex Langevin simulations of QCD at non-zero chemical potential, the Dirac operator's eigenvalues behave differently, accumulating at zero in the chiral limit, which is crucial for understanding simulation results.

Contribution

It reveals the distinct spectral behavior of the Dirac operator in complex Langevin simulations compared to traditional methods, especially at low temperatures and high chemical potentials.

Findings

Eigenvalues must be inside the quark mass at high chemical potential.

Eigenvalues accumulate at the origin in the chiral limit.

Spectral behavior differs fundamentally from standard simulations.

Abstract

We show that the spectrum of the Dirac operator in complex Langevin simulations of QCD at non-zero chemical potential must behave in a way which is radically different from the one in simulations with ordinary non-complexified gauge fields: At low temperatures the small eigenvalues of the Dirac operator must be inside the quark mass for chemical potentials as large as a third of the nucleon mass. In particular, in the chiral limit the Dirac eigenvalues of complex Langevin simulations must accumulate at the origin.