A BCS Gapped Superfluid on the Lattice

We discuss results of numerical analyses of the 3+1 dimensional Nambu--Jona-Lasinio model at non-zero baryon density. By studying relevant order parameters, it is shown that the model goes through a transition between a vacuum with broken chiral symmetry, and a chirally restored phase at high baryon chemical potential (mu) with a diquark condensate roughly proportional to the area of the Fermi surface and a broken U(1) baryon number symmetry. The condensation of diquark pairs from the fermionic spectrum is shown to lead to an energy gap (Delta) about the Fermi energy (E_F), which is found to be approximately 15% of the vacuum fermion mass and roughly independent of mu in the chirally restored phase. The ground-state is believed, therefore, to be that of a BCS superfluid. We also discuss the effect of simulating on a finite volume, and any caveats this places on the conclusions made above.