General result on charged and spin-excitation gaps in strongly correlated electron systems at half filling

The relationship between charged and spin-excitation gaps of the half-filled Hubbard model, the symmetric periodic Anderson model, and the Kondo lattice model is considered for a general d-dimensional bipartite lattice. In a previous paper [G. S. Tian, Phys. Rev. B 58, 7612 (1998)], it was shown that the quasiparticle gaps of these models at half filling are always larger than their spin excitation gaps. In the present paper, we establish a theorem, which states that the charged gap is also greater than the corresponding spin gap in these models. This conclusion, which has been reached previously for one-dimensional systems based on variational and the density-matrix renormalization-group numerical calculations, is thus put on a rigorous and more general footing.