Ferromagnetism in the Hubbard Model-- Examples from Models with Degenerate Single-Electron Ground States

TL;DR

This paper demonstrates that certain three-dimensional Hubbard models with degenerate single-electron ground states can exhibit ferromagnetism at specific electron filling levels, providing new theoretical examples of itinerant electron ferromagnetism.

Contribution

It introduces a class of Hubbard models with degenerate ground states that are proven to exhibit ferromagnetism at certain fillings, advancing understanding of itinerant electron ferromagnetism.

Findings

Ground states show ferromagnetism near specific filling factors.

Models exhibit paramagnetism at low electron fillings.

Provides finite-range ferromagnetism examples in 3D systems.

Abstract

Whether spin-independent Coulomb interaction can be the origin of a realistic ferromagnetism in an itinerant electron system has been an open problem for a long time. Here we study a class of Hubbard models on decorated lattices, which have a special property that the corresponding single-electron Schr\"{o}dinger equation has $N_{\rm d}$-fold degenerate ground states. The degeneracy $N_{\rm d}$ is proportional to the total number of sites $\abs{\Lambda}$. We prove that the ground states of the models exhibit ferromagnetism when the electron filling factor is not more than and sufficiently close to $\rho_0=N_{\rm d}/(2\abs{\Lambda})$, and paramagnetism when the filling factor is sufficiently small. An important feature of the present work is that it provides examples of three dimensional itinerant electron systems which are proved to exhibit ferromagnetism in a finite range of the electron filling factor.