Improved Mean-Field Scheme for the Hubbard Model

TL;DR

This paper introduces an improved mean-field approach for the 1-D Hubbard model that incorporates static two-particle correlations, resulting in more accurate ground state energies and density correlations compared to standard methods.

Contribution

The paper develops a mean-field scheme that includes static two-particle correlations, enhancing accuracy over traditional mean-field techniques for the Hubbard model.

Findings

Better agreement with Lanczos results for ground state energies.

Accurate on-site density-density correlations across different U values.

Improved static correlation function calculations.

Abstract

Ground state energies and on-site density-density correlations are calculated for the 1-D Hubbard model using a linear combination of the Hubbard projection operators. The mean-field coefficients in the resulting linearized Equations of Motion (EOM) depend on both one-particle static expectation values as well as static two-particle correlations. To test the model, the one particle expectation values are determined self-consistently while using Lanczos determined values for the two particle correlation terms. Ground state energies and on-site density-density correlations are then compared as a function of $U$ to the corresponding Lanczos values on a 12 site Hubbard chain for 1/2 and 5/12 fillings. To further demonstrate the validity of the technique, the static correlation functions are also calculated using a similar EOM approach, which ignores the effective vertex corrections for this problem, and compares those results as well for a 1/2 filled chain. These results show marked improvement over standard mean-field techniques.