Ferromagnetism in Hubbard Models: Low Density Route

TL;DR

This paper proves the existence of a fully polarized metallic ground state in a low-density Hubbard model, providing a new theoretical pathway to understanding ferromagnetism in strongly correlated electron systems.

Contribution

It offers the first rigorous proof of ferromagnetism in a low-density Hubbard model by mapping zigzag chains to a continuum model with Hund's coupling.

Findings

Proves a fully polarized metallic ground state at low particle densities.

Maps zigzag chains onto a continuum model with Hund's rule coupling.

Shows the maximum total spin state is the unique ground state at infinite Hubbard coupling.

Abstract

Thirty years ago the Hubbard model was introduced by Gutzwiller, Hubbard and Kanamori with the main purpose of mimicking the ferromagnetism of transition metals. Soon after, Nagaoka and Thouless pointed out a basic mechanism for ferromagnetism in strongly correlated electron systems by studying the motion of a single hole in a half--filled Hubbard model. This important work was hoped to shed light onto metallic ferromagnetism from the low doping regime. Unfortunately, this low doping route towards ferromagnetism has not been successful as far as rigorous results for finite doping concentrations are concerned. In the work presented here, we start from the opposite limit of low particle concentrations. In this limit we provide the first proof of a fully polarized metallic ground state for a Hubbard model. The proof proceeds by mapping Hubbard ``zigzag'' chains onto a continuum model with an additional degree of freedom and local first Hund's rule coupling. For this model the maximum total spin multiplet is shown to be the unique ground state for infinite Hubbard coupling. Our proof may open a low density route towards the understanding of the ferromagnetism of Hubbard models.