Thermodynamics of the two-dimensional Hubbard model in the two-body scattering approximation

Abstract: A new analytic treatment of the two-dimensional Hubbard model at finite temperature and chemical potential is presented. A next nearest neighbor hopping term of strength t' is included. This analysis is based upon a formulation of the statistical mechanics of particles in terms of the S-matrix. In the 2-body scattering approximation, the S-matrix allows a systematic expansion in t/U. We show that for U/t large enough, a region of attractive interactions exists near the Fermi surface due to 1-loop renormalization effects. For t'/t = -0.3, attractive interactions exist for U/t > 6.4. Our analysis suggests that superconductivity may not exist for t'=0. Based on the existence of solutions of the integral equation for the pseudo-energy, we provide evidence for the superconducting phase and estimate Tc/t = 0.02.