The 3 + 1 dimensional lattice NJL model at non-zero baryon density. - David Nathan Walters (2003)
Lattice simulations of the 3+1 dimensional Nambu-Jona-Lasinio model are undertaken that provide non-perturbative evidence for the existence of a BCS superfluid phase in the low temperature, high density regime. Standard analytic methods are used to fit the model's free parameters to low energy vacuum phenomenology. The model is simulated numerically for a range of baryon chemical potential mu, with the introduction of a diquark source j to allow for the observation of spontaneous U(1) global symmetry breaking in a finite volume system. For mu ≥ 0.6 inverse lattice spacings and in the limit that j → 0, a non-zero diquark condensate, a vanishing diquark susceptibility ratio and an energy gap Delta ≠ 0 about the Fermi surface in the fermion dispersion relation are all consistent with the ground-state being that of a U(l)-broken BCS superfluid. The ratio between the gap at mu = 0.8 and the vacuum fermion mass is found to be 0.15(2). This is interpreted as tentative non-perturbative evidence for the existence of a colour superconducting phase in cold, dense QCD. The effects of simulating on a finite volume, and any conditions this places on the above conclusions, are investigated. Finally, the results of some initial studies at non-zero isospin chemical potential and the prospect of simulations at non-zero temperature are discussed.