Strong coupling theory for the Hubbard model

TL;DR

This paper develops an improved strong coupling theory for the Hubbard model by extending the Hubbard-I approximation with effective particles, yielding results that closely match Quantum Monte-Carlo data.

Contribution

It introduces a novel scheme that augments the Hubbard-I approximation with composite particles, enhancing accuracy for the Hubbard model across various parameters.

Findings

Enhanced agreement with QMC results for the Green's function

Valid for both positive and negative U

Improved over traditional Hubbard-I approximation

Abstract

We reanalyze the Hubbard-I approximation by showing that it is equivalent to an effective Hamiltonian describing Fermionic charge fluctuations, which can be solved by Bogoliubov transformation. As the most important correction in the limit of large U and weak spin correlations we augment this Hamiltonian by further effective particles, which describe composite objects of a Fermionic charge fluctuation and a spin-, density- or eta- excitation. The scheme is valid for positive and negative U. We present results for the single particle Green's function for the two-dimensional Hubbard model with and without t' and t'' terms, and compare to Quantum Monte-Carlo (QMC) results for the paramagnetic phase. The overall agreement is significantly improved over the conventional Hubbard-I or two-pole approximation.