Singlet ground state of the periodic Anderson model at half filling: A rigorous result

It is proved that the ground state of the symmetric periodic Anderson model forms a total spin singlet at half filling. This result can also be applied to the Kondo lattice model, at least for the weak and the very strong antiferromagnetic-coupling limit. For the strong coupling limit of the Kondo lattice it is additionally proved that the singlet ground state exists even when two holes are doped to the half-filled band.