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

TL;DR

This paper presents an analytic approach to the 2D Hubbard model at finite temperature, revealing conditions for attractive interactions and potential superconductivity near the Fermi surface, especially with a next nearest neighbor hopping term.

Contribution

It introduces a new analytic method using the S-matrix in the 2-body scattering approximation to analyze the Hubbard model with next nearest neighbor hopping.

Findings

Attractive interactions near the Fermi surface for certain U/t and t'/t values.

Potential superconductivity with estimated Tc/t = 0.02.

Superconductivity may not occur at t' = 0.

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.