Excitation gaps in the orbitally degenerate Hubbard model

The excitation gaps for the two-orbital degenerate Hubbard model are investigated by applying a generalized version of Lieb's spin-reflection positivity. Combining the known exact results on the ground state, and making use of symmetry properties, we rigorously show that, at half-filling, the charge gaps are always larger than the spin-excitation gaps and properly defined orbital gaps.