Delocalization effect of the Hubbard repulsion in exact terms and two dimensions

TL;DR

This paper provides an exact analysis of how Hubbard repulsion U causes delocalization in a two-dimensional multiband system by reducing double occupancy and increasing localization length, based on exact ground states.

Contribution

It offers the first exact ground state analysis at half filling in two dimensions for the periodic Anderson model, elucidating the delocalization mechanism of Hubbard U.

Findings

Hubbard U acts on degenerate multiband backgrounds to induce delocalization.

Reducing double occupancy spreads ground state contributions, increasing localization length.

Results are derived from exact solutions of the two-dimensional periodic Anderson model.

Abstract

The genuine physical reasons explaining the delocalization effect of the Hubbard repulsion U are analyzed. First it is shown that always when this effect is observed, U acts on the background of a macroscopic degeneracy present in a multiband type of system. After this step I demonstrate that acting in such conditions, by strongly diminishing the double occupancy, U spreads out the contributions in the ground state wave function, hence strongly increases the one-particle localization length, consequently extends the one-particle behavior producing conditions for a delocalization effect. To be valuable, the reported results are presented in exact terms, being based on the first exact ground states deduced at half filling in two dimensions for a prototype two band system, the generic periodic Anderson model at finite value of the interaction.