Low-energy excited states in a Hubbard chain with on-site attraction

The structure and energy of the eigenstates of a 1D Hubbard Hamiltonian with negative U is studied. Solutions for the Lieb-Wu equations (1968) corresponding to U<0 are constructed from those for U>0. It is found that the ground state is continuous, while the ground-state energy, although continuous, is not analytic at the U=0 point. In the excited states, in contrast to the U>0 case, both kinds of excitation are connected with the charge distribution and the state of the spins does not affect the energy explicitly. It is also found that the distribution of parameters can change discontinuously in the excited states as U crosses zero.