The Hubbard model in the strong coupling theory at arbitrary filling

TL;DR

This paper derives and solves equations for the electron Green's function in the 2D Hubbard model using strong coupling techniques, showing good agreement with Monte Carlo data and analyzing spectral properties across various fillings and parameters.

Contribution

It introduces a self-consistent solution for the Hubbard model's Green's function at arbitrary filling using the strong coupling diagram technique, with comparisons to Monte Carlo data.

Findings

Spectral functions show qualitative and quantitative agreement with Monte Carlo results.

The Mott transition occurs near $U_c \\approx 7\\Delta/8$ at half-filling for $t'=-0.3t$.

Spectral maxima positions are close to Hubbard-I approximation predictions.

Abstract

Equations for the electron Green's function of the two-dimensional Hubbard model, derived using the strong coupling diagram technique, are self-consistently solved for different electron concentrations $n$ and tight-binding dispersions. Comparison of spectral functions calculated for the ratio of Hubbard repulsion to the nearest neighbor hopping $U/t=8$ with Monte Carlo data shows not only qualitative, but in some cases quantitative agreement in position of maxima. General spectral shapes, their evolution with momentum and filling in the wide range $0.7\lesssim n\leq 1$ are also similar. At half-filling and for the next nearest neighbor hopping constant $t'=-0.3t$ the Mott transition occurs at $U_c\approx 7\Delta/8$, where $\Delta$ is the initial bandwidth. This value is close to those obtained in the cases of the semi-elliptical density of states and for $t'=0$. In the case $U=8t$ and $t'=-0.3t$ the Mott gap reaches maximum width at $n=1.04$, and it is larger than that at $t'=0$ for half-filling. In all considered cases positions of spectral maxima are close to those in the Hubbard-I approximation.