Finite Density Lattice Gauge Theories with Positive Fermion Determinants

TL;DR

This paper investigates phase transitions in finite density lattice gauge theories, specifically QCD with two flavors and two colors, analyzing how chemical potential influences superfluid states and symmetry breaking at finite temperature.

Contribution

It provides new simulation results on the finite temperature phase transitions and the nature of the superfluid states in finite density lattice gauge theories with positive fermion determinants.

Findings

At $_I < m_$, the transition is a crossover with no critical endpoint.

For $_I > m_$, a true phase transition occurs, changing from second to first order as $_I$ increases.

Spectrum analysis reveals Goldstone and pseudo-Goldstone bosons related to symmetry breaking.

Abstract

We perform simulations of (3-colour) QCD with 2 quark flavours at a finite chemical potential $\mu_I$ for isospin($I_3$), and of 2-colour QCD at a finite chemical potential $\mu$ for quark number. At zero temperature, QCD at finite $\mu_I$ has a mean-field phase transition at $\mu_I=m_\pi$ to a superfluid state with a charged pion condensate which spontaneously breaks $I_3$. We study the finite temperature transition as a function of $\mu_I$. For $\mu_I < m_\pi$, where this is closely related to the transition at finite $\mu$, this appears to be a crossover independent of quark mass, with no sign of the proposed critical endpoint. For $\mu_I > m_\pi$ this becomes a true phase transition where the pion condensate evaporates. For $\mu_I$ just above $m_\pi$ the transition seems to be second order, while for larger $\mu_I$ it appears to become first order. At zero temperature, 2-colour QCD also possesses a superfluid state with a diquark condensate. We study its spectrum of Goldstone and pseudo-Goldstone bosons associated with chiral and quark-number symmetry breaking.