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.

Figure 1

The square lattice with the quasi-1D band structure of the $p$-orbital bands. Particles in the $p_x$ $(p_y)$ orbital can only move along the $x$ $(y)$ direction, respectively. The sign of $t_{\parallel }$ can be changed by a gauge transformation on the square lattice.