Strong-coupling expansion for the Hubbard model in arbitrary dimension using slave bosons

TL;DR

This paper develops a strong-coupling expansion for the Hubbard model's antiferromagnetic phase using slave-boson mean-field theory, providing accurate energy estimates up to fifth order in arbitrary dimensions.

Contribution

It introduces a novel strong-coupling expansion method based on moments of the density of states, applicable to hypercubic lattices in any dimension, with improved accuracy over previous approaches.

Findings

Energy accuracy better than 1% for U/t ≥ 8

Expansion valid up to fifth order in t/U

Comparison with previous perturbation methods included

Abstract

A strong-coupling expansion for the antiferromagnetic phase of the Hubbard model is derived in the framework of the slave-boson mean-field approximation. The expansion can be obtained in terms of moments of the density of states of freely hopping electrons on a lattice, which in turn are obtained for hypercubic lattices in arbitrary dimension. The expansion is given for the case of half-filling and for the energy up to fifth order in the ratio of hopping integral $t$ over on-site interaction $U$, but can straightforwardly be generalized to the non-half-filled case and be extended to higher orders in $t/U$. For the energy the expansion is found to have an accuracy of better than $1 \%$ for $U/t \geq 8$. A comparison is given with an earlier perturbation expansion based on the Linear Spin Wave approximation and with a similar expansion based on the Hartree-Fock approximation. The case of an infinite number of spatial dimensions is discussed.