ON THE ONE-DIMENSIONAL HUBBARD-MODEL AWAY FROM HALF-FILLING

We study the spectrum of the one-dimensional Hubbard model near the half-filled band, i.e. for electronic density n = 1 - delta, delta << 1, and also in the low-density limit n << 1. Ground state and excited states are described by integral equations which are derived from the Bethe Ansatz. These equations, which can be solved analytically only in the case of half-filling (delta = 0), are investigated systematically in both limits delta << 1, n << 1. Appropriate expansions of the momenta and energies of the ground state and the excited states as well as correlation exponents are determined.