We identify the global symmetries of SU(2) lattice gauge theory with N flavors of staggered fermion in the presence of a quark chemical potential µ, for fermions in both fundamental and adjoint representations, and anticipate likely patterns of symmetry breaking at both low and high densities. Results from numerical simulations of the model with N = 1 adjoint flavor on a 4 3 × 8 lattice are presented, using both hybrid Monte Carlo and Two-Step Multi-Boson algorithms. It is shown that the sign of the fermion determinant starts to fluctuate once the model enters a phase with non-zero baryon charge density. HMC simulations are not ergodic in this regime, but TSMB simulations retain ergodicity even in the dense phase, and in addition appear to show superior decorrelation. The HMC results for the equation of state and the pion mass show good quantitative agreement with the predictions of chiral perturbation theory, which should hold only for N ≥ 2. The TSMB results incorporating the sign of the determinant support a delayed onset transition, consistent with the pattern of symmetry breaking expected for N = 1.

We study SU(2) Lattice Gauge Theory with dynamical fermions at nonzero chemical potential µ. The symmetries special to SU(2) for staggered fermions on the lattice are discussed explicitly and their relevance to spectroscopy and condensates at non-zero chemical potential are considered. Using the molecular dynamics algorithm on small lattices we find qualitative changes in the theory's spectroscopy at small and large values of µ. This preliminary study should lay the groundwork for future large scale simulations.

We have simulated two-colour four-flavour QCD at non-zero chemical potential µ for quark number. Simulations were performed on 8 4 and 12 3 × 24 lattices. Clear evidence was seen for the formation of a colourless diquark condensate which breaks quark number spontaneously, for µ > µ c ∼ m π /2.The transition appears to be second order. We have measured the spectrum of scalar and pseudoscalar bosons which shows clear evidence for the expected Goldstone boson. Our results are in qualitative agreement with those from effective Lagrangians for the potential Goldstone excitations of this theory.