Metallic ferromagnetism supported by a single band in a multi-band Hubbard model

TL;DR

This paper constructs a multi-band Hubbard model on decorated lattices and proves that its ground states exhibit metallic ferromagnetism under certain conditions related to the number of holes and system size.

Contribution

The paper provides a rigorous proof of metallic ferromagnetism in a multi-band Hubbard model with a single active band, extending understanding of ferromagnetic ground states.

Findings

Ground states exhibit saturated ferromagnetism when holes are sufficiently few.

Ferromagnetism persists even with a larger number of holes, under specific size conditions.

The results offer a rigorous example of metallic ferromagnetism in lattice models.

Abstract

We construct a multi-band Hubbard model on the lattice obtained by "decorating" a closely packed $d$-dimensional lattice $\mathcal{M}$ (such as the triangular lattice) where $d\ge2$. We take the limits in which the Coulomb interaction and the band gap become infinitely large. Then there remains only a single band with finite energy, on which electrons are supported. Let the electron number be $N_\mathrm{e}=|\mathcal{M}|-N_\mathrm{h}$, where $|\mathcal{M}|$ corresponds to the electron number which makes the lowest (finite energy) band half-filled, and $N_\mathrm{h}$ is the number of "holes". It is expected that the model exhibits metallic ferromagnetism if $N_\mathrm{h}/|\mathcal{M}|$ is nonvanishing but sufficiently small. We prove that the ground states exhibit saturated ferromagnetism if $N_\mathrm{h}\le(\text{const.})|\mathcal{M}|^{2/(d+2)}$, and exhibit (not necessarily saturated) ferromagnetism if $N_\mathrm{h}\le(\mathrm{const.})|\mathcal{M}|^{(d+1)/(d+2)}$. This may be regarded as a rigorous example of metallic ferromagnetism provided that the system size $|\mathcal{M}|$ is not too large.