Hubbard models with nearly flat bands: Ground-state ferromagnetism driven by kinetic energy

TL;DR

This paper investigates how kinetic energy, introduced by slight dispersion in flat bands of Hubbard models, can induce ground-state ferromagnetism, with findings showing various dependencies on bandwidth and interaction strength.

Contribution

It demonstrates that dispersive flat bands in Hubbard models can lead to ferromagnetism driven by kinetic energy, expanding understanding beyond traditional flat-band ferromagnetism models.

Findings

Small dispersion can induce ferromagnetism at large U.

Ferromagnetism can appear at very small U in some cases.

Critical bandwidth influences the emergence of ferromagnetism.

Abstract

We consider the standard repulsive Hubbard model with a flat lowest-energy band for two one-dimensional lattices (diamond chain and ladder) as well as for a two-dimensional lattice (bilayer) at half filling of the flat band. The considered models do not fall in the class of Mielke-Tasaki flat-band ferromagnets, since they do not obey the connectivity conditions. However, the ground-state ferromagnetism can emerge, if the flat band becomes dispersive. To study this kinetic-energy-driven ferromagnetism we use perturbation theory and exact diagonalization of finite lattices. We find as a typical scenario that small and moderate dispersion may lead to a ferromagnetic ground state for sufficiently large on-site Hubbard repulsion $U>U_c$, where $U_c$ increases monotonically with the acquired bandwidth. However, we also observe for some specific parameter cases, that (i) ferromagnetism appears at already very small $U_c$, (ii) ferromagnetism does not show up at all, (iii) the critical on-site repulsion $U_c$ is a nonmonotonic function of the bandwidth, or that (iv) a critical bandwidth is needed to open the window for ground-state ferromagnetism.