Charged and spin-excitation gaps in half-filled strongly correlated   electron systems: A rigorous result
  By exploiting the particle-hole symmetries of the Hubbard model, the periodic Anderson model and the Kondo lattice model at half-filling and applying a generalized version of Lieb's spin-reflection positivity method, we show that the charged gaps of these models are always larger than their spin excitation gaps. This theorem confirms the previous results derived by either the variational approach or the density renormalization group approach. 
Guang-Shan Tian