Exact Results of Itinerant Ferromagnetism in Multi-orbital Hubbard Systems

We study itinerant ferromagnetism in multi-orbital 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 any generic filling factor {\$}0 \textless n \textless 2 (0 \textless n \textless 3){\$} in two (three) dimensions. This theorem applies to both certain d-orbital transition-metal oxide layer systems and the p-orbital bands with ultra-cold fermions in optical lattices