The Hubbard Model: A Computer Lab in the Strong Coupling Region

TL;DR

This paper introduces a rigorous computational test for solutions of the Hubbard Model in the strong coupling regime, revealing significant issues in mean field and one-dimensional solutions and proposing a method to identify the most accurate spectral weight function.

Contribution

It presents a new computational 'Computer Lab' test based on exact strong coupling results to evaluate and improve solutions of the Hubbard Model.

Findings

Mean field solutions show substantial problems.

One-dimensional solutions also exhibit issues.

The method helps identify the most accurate spectral weight function.

Abstract

A challenge - and opportunity - is offered to the Hubbard Model community of solutions extant for the strong coupling region. A rigorous and quantitatively demanding test - a Computer Lab - is presented based on certain exact results for the strong coupling limit derived in a companion paper. The test offers rich insights into the essential physics of the model, specifically the quasiparticle energy and width of the spectral weight function in the lower Hubbard band. The width of the spectral weight function, related to electron scattering, is large and has a strong momentum dependence, even for infinite coupling. The test is applied to mean field solutions as well as some one dimensional results. In each case, substantial problems are exposed. The method is also used to determine a "best" (i.e. moment preserving) solution, subject to only one assumption of a single dominant peak for the lower Hubbard band spectral weight function.