On the ground state and excitations of a four-component fermion model
  The properties of the ground state and excitations of a four-component Hubbard-like model are studied by the Lieb-Schultz-Mattis approach. It is proven rigorously that the ground state of the model is nondegenerate and excitations are gapless at all band fillings. 
You-Quan Li, Guan-Shan Tian, Michael Ma, and Hai-Qing Lin