Characteristics of the eigenvalue distribution of the Dirac operator in dense two-color QCD

TL;DR

This paper investigates the eigenvalue distribution of the lattice Dirac operator in two-color QCD at finite chemical potential, relating spectral properties to phase transitions and condensates through extended Banks-Casher relations.

Contribution

It provides explicit calculations of eigenvalues at finite density, extends Banks-Casher relations to the complex plane, and analyzes spectral changes across phase transitions in two-color QCD.

Findings

Eigenvalue spectral density relates to physical condensates.

Spectral changes correspond to phase transitions.

Artificial pion condensation is not density-induced in strong-coupling two-color QCD.

Abstract

We exposit the eigenvalue distribution of the lattice Dirac operator in Quantum Chromodynamics with two colors (i.e. two-color QCD). We explicitly calculate all the eigenvalues in the presence of finite quark chemical potential \mu for a given gauge configuration on the finite-volume lattice. First, we elaborate the Banks-Casher relations in the complex plane extended for the diquark condensate as well as the chiral condensate to relate the eigenvalue spectral density to the physical observable. Next, we evaluate the condensates and clarify the characteristic spectral change corresponding to the phase transition. Assuming the strong coupling limit, we exhibit the numerical results for a random gauge configuration in two-color QCD implemented by the staggered fermion formalism and confirm that our results agree well with the known estimate quantitatively. We then exploit our method in the case of the Wilson fermion formalism with two flavors. Also we elucidate the possibility of the Aoki (parity-flavor broken) phase and conclude from the point of view of the spectral density that the artificial pion condensation is not induced by the density effect in strong-coupling two-color QCD.