Continuum Goldstone spectrum of two-color QCD at finite density with staggered quarks

TL;DR

This study uses lattice simulations to show that two-color QCD with staggered quarks exhibits a continuum Goldstone spectrum consistent with the Gaussian orthogonal ensemble when monopoles are suppressed, correcting earlier unphysical behavior.

Contribution

It demonstrates that the unphysical GSE spectrum observed in previous simulations is due to monopole-rich bulk phases and that improved actions can recover the physical GOE spectrum in the continuum limit.

Findings

Unphysical GSE spectrum occurs in the bulk phase with high monopole density.

Suppressing monopoles with improved actions restores the GOE spectrum.

Eigenvalue distributions shift from GSE to GOE as monopoles are suppressed.

Abstract

We carry out lattice simulations of two-color QCD and spectroscopy at finite density with two flavors of rooted-staggered quarks and a diquark source term. As in a previous four-flavor study, for small values of the inverse gauge coupling we observe a Goldstone spectrum which reflects the symmetry-breaking pattern of a Gaussian symplectic chiral random-matrix ensemble (GSE) with Dyson index $\beta_D=4$, which corresponds to any-color QCD with adjoint quarks in the continuum instead of QC$_2$D wih fundamental quarks. We show that this unphysical behavior occurs only inside of the bulk phase of $SU(2)$ gauge theory, where the density of $Z_2$ monopoles is high. Using an improved gauge action and a somewhat larger inverse coupling to suppress these monopoles, we demonstrate that the continuum Goldstone spectrum of two-color QCD, corresponding to a Gaussian orthogonal ensemble (GOE) with Dyson index $\beta_D=1$, is recovered also with rooted-staggered quarks once simulations are performed away from the bulk phase. We further demonstrate how this change of random-matrix ensemble is reflected in the distribution of eigenvalues of the Dirac operator. By computing the unfolded level spacings inside and outside of the bulk phase, we demonstrate that, starting with the low-lying eigenmodes which determine the infrared physics, the distribution of eigenmodes continuously changes from the GSE to the GOE one as monopoles are suppressed.