The Hubbard Model: Exact Results in the Strong Coupling Limit

TL;DR

This paper derives exact relations for the spectral weight function of the Hubbard model at infinite U, providing insights into strong correlation effects without approximations across any lattice and dimension.

Contribution

It presents a novel, exact derivation of spectral weight moments in the Hubbard model's strong coupling limit, avoiding common approximations and applicable to any lattice structure.

Findings

Exact relations for spectral weight moments are derived.

Relations involve moments over the low energy spectrum only.

Second central moment remains large near half-filling.

Abstract

Exact relations are derived for the Fermi Hubbard spectral weight function for infinite U at zero temperature in the thermodynamic limit for any dimension,any lattice structure and general hopping matrix. These relations involve moments of the spectral weight function but differ from similar work by (a) restricting the moments over the interesting low energy (lower Hubbard band) spectrum and (b) without any of the usual approximations (e.g. decoupling) for the requisite higher order correlation functions. The latter are determined exactly as explicit functions of the single particle correlation function in the infinite U limit. The methods behind these results have the additional virtue of simplicity - cumbersome, but entirely straightforward. In a companion paper, the relations offer rich insights into the model behavior and offer severe tests - a computer lab - of any proposed solution to the Hubbard model in the strong correlation (large finite U) region. As the electron density approaches one electron per site, then the correlation functions become local, so are trivial to compute exactly. In that limit and for the paramagnetic case, the second central moment of the spectral weight function is not zero, but quite large.