Ferromagnetically ordered metal in the single-band hubbard model

Akinori Tanaka, Hal Tasaki

Koichi Kusakabe, Hideo Aoki

Michael Plischke

H. Capellmann

Andreas Mielke

A Hubbard model with a single, partially flat band has ferromagnetic ground states. It is shown that local stability of ferromagnetism implies its global stability in such a model: The model has only ferromagnetic ground states if there are no single spin-flip ground states. Since a single-band Hubbard model away from half filling describes a metal, this result may open a route to metallic ferromagnetism in single-band Hubbard models.

Akinori Tanaka, Hal Tasaki

We present the first rigorous example of the Hubbard model in any dimension which exhibits metallic ferromagnetism. The model is a genuine Hubbard model with short-range hopping and on-site Coulomb repulsion, and has many single-electron bands. In the limit where the band gap and the Coulomb repulsion become infinite, we prove that the ground states are completely ferromagnetic and at the same time conducting.