Strong coupling expansion of the Kondo lattice model

The Kondo lattice model is an extension to a lattice of the one impurity model. This model has been introduced to describe heavy-fermions systems. We study this model in the special case of half-filling of the conduction band. We apply a general perturbation method in t/J, where J is the antiferromagnetic Kondo interaction and t the hopping parameter for the conduction electrons. The double occupancy, the on-site total spin and the charge and spin gaps are obtained to lower order in t J.