Abundance of Ground States with Positive Parity

We investigate analytically and numerically a random-matrix model for m fermions occupying l1 single-particle states with positive parity and l2 single-particle states with negative parity and interacting through random two-body forces that conserve parity. The single-particle states are completely degenerate and carry no further quantum numbers. We compare spectra of many-body states with positive and with negative parity. We show that in the dilute limit, ground states with positive and with negative parity occur with equal probability. Differences in the ground-state probabilities are, thus, a finite-size effect and are mainly due to different dimensions of the Hilbert spaces of either parity.