GROUND-STATE AND ELEMENTAL EXCITATIONS OF THE ONE-DIMENSIONAL MULTICOMPONENT FERMI GAS WITH DELTA-FUNCTION INTERACTION

We consider a gas of fermions with parabolic dispersion and N spin com ponents (or spin S, N = 2S + 1) with SU(N) symmetry in one dimension i nteracting via a delta-function potential. The model is integrable and its solution has been obtained by Sutherland in terms of N nested Bet he ansatze. The ground-state Bethe ansatz integral equations are solve d numerically for both repulsive and attractive interactions to obtain the energy, the chemical potential, and the magnetic susceptibility a s a function of the band filling and the interaction strength. For the repulsive interaction the Fermi gas has the properties of a Luttinger liquid. In the attractive case, on the other hand, the fermions in th e ground-state form bound states of up to N fermions of different spin components, The spectrum of elemental charge and spin excitations is derived for the repulsive and attractive situations. The spectrum is d iscussed in the limits of vanishing interaction strength and very stro ng coupling. For the repulsive interaction the low-lying charge excita tions can be characterized by the Fermi momentum and the Fermi velocit y. The range of the spin-wave excitations is correlated with the Fermi momentum of the charges. The spin-wave velocity is inversely proporti onal to the magnetic susceptibility. The spin-wave excitations become soft in the infinite-repulsive-coupling limit. In the attractive case in zero field all excitation branches except that of bound states of N fermions have an energy gap. It requires a finite energy to break the se bound states and hence there is no response to a field smaller than a critical field. The low-T specific heat is proportional to the temp erature.