Stability of ferromagnetism in the Hubbard model on the kagom\'e lattice

TL;DR

This paper investigates the stability of ferromagnetism in a perturbed Hubbard model on the kagomé lattice, demonstrating that ferromagnetic ground states persist even when the flat band becomes dispersive.

Contribution

It proves that ferromagnetism remains stable in the Hubbard model on the kagomé lattice under certain perturbations that make the flat band dispersive.

Findings

Ferromagnetism persists at half-filling despite band dispersion.

Ground states remain saturated ferromagnetic when the lowest band is nearly flat.

The model extends previous flat-band ferromagnetism results to perturbed cases.

Abstract

The Hubbard model on the kagom\'e lattice has highly degenerate ground states (the flat lowest band) in the corresponding single-electron problem and exhibits the so-called flat-band ferromagnetism in the many-electron ground states as was found by Mielke. Here we study the model obtained by adding extra hopping terms to the above model. The lowest single-electron band becomes dispersive, and there is no band gap between the lowest band and the other band. We prove that, at half-filling of the lowest band, the ground states of this perturbed model remain saturated ferromagnetic if the lowest band is nearly flat.