THERMODYNAMICS OF THE ONE-DIMENSIONAL MULTICOMPONENT FERMI GAS WITH A DELTA-FUNCTION INTERACTION

We consider a gas of fermions with parabolic dispersion and N spin-components (or spin S, N = 2S + 1) with SU(N) symmetry in one dimension interacting via a delta-function potential. The model is integrable and its solution has been obtained by Sutherland in terms of N nested Bethe ansatze. We analyse the discrete Bethe ansatz equations and classify their solutions according to the string hypothesis. The thermodynamic Bethe-ansatz equations are derived for arbitrary band-filling for both repulsive and attractive interaction in terms of the thermodynamic energy potentials for the classes of eigenstates of the Hamiltonian. These equations are then discussed in several limiting cases, e.g. S = 1/2, the ground state (T --> 0), for vanishing interaction strength, for strong coupling, in the high-temperature limit, and the large-N limit.