Chiral Symmetry Breaking and the Dirac Spectrum at Nonzero Chemical Potential

TL;DR

This paper explores how the spectral density of the QCD Dirac operator at nonzero chemical potential relates to chiral symmetry breaking, revealing that oscillations in the eigenvalue density drive the discontinuity in the chiral condensate.

Contribution

It provides an analytical analysis of the eigenvalue density oscillations at nonzero chemical potential and their role in chiral symmetry breaking, extending beyond microscopic regimes.

Findings

Oscillations in eigenvalue density have a period scaling as 1/V.

Amplitude of oscillations diverges exponentially with volume.

Discontinuity in chiral condensate is due to oscillating regions, not eigenvalue accumulation.

Abstract

The relation between the spectral density of the QCD Dirac operator at nonzero baryon chemical potential and the chiral condensate is investigated. We use the analytical result for the eigenvalue density in the microscopic regime which shows oscillations with a period that scales as 1/V and an amplitude that diverges exponentially with the volume $V=L^4$. We find that the discontinuity of the chiral condensate is due to the whole oscillating region rather than to an accumulation of eigenvalues at the origin. These results also extend beyond the microscopic regime to chemical potentials $\mu \sim 1/L$.