2-DIMENSIONAL HUBBARD-MODEL AT LOW ELECTRON-DENSITY

The two dimensional Hubbard model with repulsive interaction is studied in the t-matrix approximation, which is the valid approximation in low electron density. The particle-particle correlation function and the t-matrix are obtained analytically. By use of these analytical results it is shown that the t-matrix and hence the self-energy have no singularities in the upper half plane of the complex energy variable. The phase angle delta(2k(F) + q, omega), with k(F) being the Fermi wave vector, in the limit of q = 0 and omega = 0 is found to depend strongly on the ratio omega/q and is not always zero. The case of the attractive interaction is also briefly studied.