Two-body scattering phase shifts in the Hubbard model

The solution of the two electron problem in a Hubbard model embedded in a Fermi sea is obtained in arbitrary dimension. The ground state energy and excited states are calculated. In the one-dimensional case it is shown that the excitation states coincide with the well-known Bethe ansatz solution. In two dimensions, these states can be expressed by an elliptic integral of the first kind, while in three dimensions by a hypergeometric function of three variables (Lauricella function). In two dimensions many similarities with a Luttinger liquid phase are obtained for a specific domain of the wave vectors: namely the ground state is an extended state with a well-defined phase shift.