Ferromagnetism in the Hubbard model: A constructive approach

TL;DR

This paper presents a rigorous constructive approach to demonstrate saturated ferromagnetism in a class of nonsingular Hubbard models, advancing understanding of itinerant electron ferromagnetism with spin-independent interactions.

Contribution

It introduces a new class of nonsingular Hubbard models and proves their ground states exhibit saturated ferromagnetism, providing a rigorous foundation for itinerant electron ferromagnetism.

Findings

Ground states show saturated ferromagnetism with maximum total spins.

Models are nonsingular with finite Coulomb interaction and density of states.

Results establish low energy behavior as a ferromagnetic insulator.

Abstract

It is believed that strong ferromagnetic orders in some solids are generated by subtle interplay between quantum many-body effects and spin-independent Coulomb interactions between electrons. Here we describe our rigorous and constructive approach to ferromagnetism in the Hubbard model, which is a standard idealized model for strongly interacting electrons in a solid. We introduce a class of Hubbard models in any dimensions which are nonsingular in the sense that both the Coulomb interaction and the density of states (at the Fermi level) are finite. We then prove that the ground states of the models exhibit saturated ferromagnetism, i.e., have maximum total spins. Combined with our earlier results, the present work provides nonsingular models of itinerant electrons with only spin-independent interactions where low energy behaviors are proved to be that of a ``healthy'' ferromagnetic insulator.