Ferromagnetism in the Hubbard model with a gapless nearly-flat band

TL;DR

This paper introduces a three-dimensional Hubbard model with a gapless nearly-flat band that demonstrates ferromagnetism at half-filling, providing a new example of ferromagnetic ground states in such models.

Contribution

The paper constructs a simple, three-dimensional lattice Hubbard model with a gapless nearly-flat band and proves ferromagnetism occurs under certain conditions, a novel result in non-singular models.

Findings

Ground state is unique and ferromagnetic at half-filling.

Ferromagnetism occurs when the band is nearly flat and interaction strength exceeds a threshold.

First example of ferromagnetism in 3D non-singular gapless models.

Abstract

We present a version of the Hubbard model with a gapless nearly-flat lowest band which exhibits ferromagnetism in two or more dimensions. The model is defined on a lattice obtained by placing a site on each edge of the hypercubic lattice, and electron hopping is assumed to be only between nearest and next nearest neighbor sites. The lattice, where all the sites are identical, is simple, and the corresponding single-electron band structure, where two cosine-type bands touch without an energy gap, is also simple. We prove that the ground state of the model is unique and ferromagnetic at half-filling of the lower band, if the lower band is nearly flat and the strength of on-site repulsion is larger than a certain value which is independent of the lattice size. This is the first example of ferromagnetism in three dimensional non-singular models with a gapless band structure.