A self-energy for the intermediate valence model

The authors present a somewhat unorthodox approach to the periodic Anderson model in which both the on-site correlation and the single-particle hybridisation terms are included in the perturbation. They show that it is possible to utilise the known exact solutions for the cases where either the on-site correlation or hybridisation is zero and make use of the definition of irreducibility for mixed species graphs, to show how a sum over all graphs can be attempted for both localised and conduction electron propagators. The results are internally consistent and in particular they find that the energy of the system can be determined either by thermal averaging the Hamiltonian or from a density-of-states picture. For a particular choice of parameters it is statistically favourable to make a comparison with the exact results for a three-site, six-electron model and for this system the number of localised holes and the specific heat have been calculated numerically.