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

TL;DR

This study uses self-consistent second order perturbation theory to analyze the Hubbard model in two dimensions, revealing how doping affects mass enhancement, Fermi surface anisotropy, and density of states within a weak coupling Fermi liquid framework.

Contribution

It applies SCSOPT to the 2D Hubbard model across doping levels, providing detailed insights into mass enhancement and Fermi surface anisotropy effects.

Findings

Mass enhancement factor increases as doping decreases.

Fermi surface anisotropy is enhanced at higher densities and suppressed at lower densities.

Density of states at the Fermi level is reduced due to k-mass suppression.

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 $\omega$-mass enhancement factor increases, while k-mass enhancement factor decreases. The increase in $\omega$-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.