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.
Highlights
The QCD phase diagram continues to be the subject of intense theoretical and experimental studies
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 βD 1⁄4 1, is recovered with rooted-staggered quarks once simulations are performed away from the bulk phase
By computing the unfolded level spacings inside and outside of the bulk phase, we demonstrate that, starting with the lowlying eigenmodes which determine the infrared physics, the distribution of eigenmodes continuously changes from the Gaussian symplectic chiral random-matrix ensemble (GSE) to the GOE one as monopoles are suppressed
Summary
The QCD phase diagram continues to be the subject of intense theoretical and experimental studies. The effective field theory prediction for the Goldstone spectrum with the Uð2Þ → Uð1Þ chiral symmetry breaking of the fundamental staggered two-color action was explicitly worked out in [3]. We will find that inside the bulk phase, the Goldstone spectrum for Dyson index βD 1⁄4 4 as for adjoint continuum quarks is reproduced, while outside the bulk phase we observe the correct Goldstone spectrum of two-color QCD, corresponding to the Dyson index βD 1⁄4 1 of the continuum Dirac operator, with rooted-staggered quarks.
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