Metallic ferromagnetism in the Hubbard model: A rigorous example

TL;DR

This paper provides a rigorous mathematical example of a Hubbard model that simultaneously exhibits metallic ferromagnetism, demonstrating the coexistence of ferromagnetism and conductivity in a specific quantum many-body system.

Contribution

It presents the first rigorous proof of metallic ferromagnetism in a genuine Hubbard model with short-range hopping and multiple bands.

Findings

Ground states are fully ferromagnetic.

Ground states are conducting.

Model is a genuine Hubbard model with short-range interactions.

Abstract

We present the first rigorous example of the Hubbard model in any dimensions which exhibits metallic ferromagnetism. The model is a genuine Hubbard model with short-range hopping and on-site Coulomb repulsion, and has multi single-electron bands. In the limit where the band gap and the Coulomb repulsion become infinite, we prove that the ground states are completely ferromagnetic and at the same time conducting.