Self-Consistent Second Order Perturbation Theory for the Hubbard Model in Two Dimensions

Abstract

We apply self-consistent second order perturbation theory (SCSOPT) with respect to the on-site repulsive interaction U to study the Hubbard model in two dimensions. We investigate single particle properties of the model over the entire doping range at zero temperature. It is shown that as doping decreases toward half-filling $ω$-mass enhancement factor increases, while k-mass enhancement factor decreases. The increase in $ω$-mass enhancement factor is larger than the decrease in k-mass enhancement factor, so that total-mass is larger than that in the non-interacting case. When particle number density per unit cell n is given by 0.64<n<1.0 interaction enhances anisotropy of the Fermi surface, whereas at lower densities n<0.64 interaction suppresses anisotropy of it. Due to the decrease in k-mass enhancement factor the density of states (DOS) at the Fermi level is suppressed. It is possible to understand the results within the framework of the weak coupling Fermi liquid theory.