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 ${\mu }_I$ 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.

Comments: 12 pages Latex/ptptex, 10 figures. Talk at Finite Density QCD, 2003, Nara Revised to add 2 references