Fourth-order effective Hamiltonian for the Anderson lattice

A canonical transformation of the Schrieffer-Wolff type is applied to the periodic Anderson model. The case of infinitely correlated $f$-like orbitals is dealt with, and these are described through standard basis operators, including spin degeneracy only. First- and third-order terms in the mixing parameter are eliminated. The resulting Hamiltonian contains terms up to fourth order. These describe several interaction processes including intersite spin and charge correlations, conduction-electron scattering, and excitonic interactions. A detailed analysis of the modified Ruderman-Kittel-Kasuya-Yosida interaction obtained is given. Possible extensions of some of the results to higher orders are discussed. The method provides a way to evaluate the spin and charge susceptibilities of the conduction-electron gas in this model. The possible relevance of these functions to a theory of the phonon spectrum and of magnetic ordering of intermediate-valence systems is mentioned.