Exact results for itinerant ferromagnetism in multiorbital systems on square and cubic lattices

We study itinerant ferromagnetism in multiorbital Hubbard models in certain two-dimensional square and three-dimensional cubic lattices. In the strong coupling limit where doubly occupied orbitals are not allowed, we prove that the fully spin-polarized states are the unique ground states, apart from the trivial spin degeneracies, for a large region of filling factors. Possible applications to p-orbital bands with ultracold fermions in optical lattices, and electronic 3d-orbital bands in transition-metal oxides, are discussed.