Finite Density Lattice Gauge Theories with Positive Fermion Determinants

Abstract

We perform simulations of (3-colour) QCD with 2 quark flavours at a finite chemical potential $μ_I$ for isospin($I_3$), and of 2-colour QCD at a finite chemical potential $μ$ for quark number. At zero temperature, QCD at finite $μ_I$ has a mean-field phase transition at $μ_I=m_π$ to a superfluid state with a charged pion condensate which spontaneously breaks $I_3$. We study the finite temperature transition as a function of $μ_I$. For $μ_I < m_π$, where this is closely related to the transition at finite $μ$, this appears to be a crossover independent of quark mass, with no sign of the proposed critical endpoint. For $μ_I > m_π$ this becomes a true phase transition where the pion condensate evaporates. For $μ_I$ just above $m_π$ the transition seems to be second order, while for larger $μ_I$ 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.