Effect of the exchange hole on the Gutzwiller approximation in one dimension

TL;DR

This paper improves the Gutzwiller approximation in one dimension by incorporating the correct exchange hole, resulting in more accurate predictions for the Hubbard model's properties.

Contribution

The authors implement the correct exchange hole form into the Gutzwiller approximation, enhancing its accuracy in one-dimensional systems.

Findings

Gutzwiller approximation aligns closely with full wavefunction results after correction.

Metallicity and anti-ferromagnetism are accurately recovered.

Improved approximation works well for the 1D Hubbard model at half-filling.

Abstract

The Gutzwiller approximate solution to the Gutzwiller wavefunction yields exact results for the Gutzwiller wavefunction in the infinite dimensional limit. Implicit in the Gutzwiller approximation is an approximate local form of the fermion exchange hole. This approximate form is the same for all dimensions but is incorrect except in infinite dimensions. We implement the correct form for the exchange hole into the Gutzwiller approximation. We perform calculations on the one-dimensional Hubbard model at half-filling. They indicate that the implementation of the exchange hole already brings the Gutzwiller approximation into very close quantitative agreement with the results of the full Gutzwiller wavefunction. Metallicity as well as anti-ferromagnetism are recovered.