Ferromagnetism in multi-band Hubbard models

Abstract

A constructive approach is presented to study the ferromagnetism in multi-band Hubbard models whose Hamiltonians consist of an electron hopping and an on-site Coulomb interaction. We prove that the models have the fully ferromagnetized ground states if the strength of the on-site Coulomb interaction is larger than a certain value. The models are based on the recently proposed (nearly) flat-band models, but they have some physically different features; in our models effective inter-band interactions which are derived from the combination of the electron hopping and the on-site Coulomb interaction play a crucial role in generating the ferromagnetism. We also introduce another type of multi-band Hubbard model which has two orbital states at each site and interactions between these two states in addition to the electron hopping and the Coulomb repulsion of two electrons on the same state, and show that the ground states of the model also exhibit the ferromagnetism. We stress that there is no need to take any strong coupling limit, such as an infinite on-site Coulomb interaction, in the proofs of the ferromagnetism in the ground states for both types of the multi-band Hubbard models.