Phase Diagram of the Dirac Spectrum at Nonzero Chemical Potential

TL;DR

This paper derives the phase diagram of the Dirac spectrum in QCD at nonzero chemical potential, revealing regions of constant density, oscillations, and zeros, linked to different condensed phases.

Contribution

It provides a theoretical derivation of the Dirac spectrum phase diagram using a chiral Lagrangian, connecting spectral regions to pion and kaon condensation.

Findings

Constant eigenvalue density indicates a pion condensed phase.

Oscillatory eigenvalue density corresponds to a kaon condensed phase.

Normal phase with chiral condensate has no eigenvalues in the complex plane.

Abstract

The Dirac spectrum of QCD with dynamical fermions at nonzero chemical potential is characterized by three regions, a region with a constant eigenvalue density, a region where the eigenvalue density shows oscillations that grow exponentially with the volume and the remainder of the complex plane where the eigenvalue density is zero. In this paper we derive the phase diagram of the Dirac spectrum from a chiral Lagrangian. We show that the constant eigenvalue density corresponds to a pion condensed phase while the strongly oscillating region is given by a kaon condensed phase. The normal phase with nonzero chiral condensate but vanishing Bose condensates coincides with the region of the complex plane where there are no eigenvalues.