Renormalization of the periodic Anderson model: an alternative analytical approach to heavy Fermion behavior

Abstract

In this paper a recently developed projector-based renormalization method (PRM) for many-particle Hamiltonians is applied to the periodic Anderson model (PAM) with the aim to describe heavy Fermion behavior. In this method high-energetic excitation operators instead of high energetic states are eliminated. We arrive at an effective Hamiltonian for a quasi-free system which consists of two non-interacting heavy-quasiparticle bands. The resulting renormalization equations for the parameters of the Hamiltonian are valid for large as well as small degeneracy $ν_f$ of the angular momentum. An expansion in $1/ν_f$ is avoided. Within an additional approximation which adapts the idea of a fixed renormalized \textit{f} level $\tildeε_{f}$, we obtain coupled equations for $\tildeε_{f}$ and the averaged \textit{f} occupation $ $. These equations resemble to a certain extent those of the usual slave boson mean-field (SB) treatment. In particular, for large $ν_f$ the results for the PRM and the SB approach agree perfectly whereas considerable differences are found for small $ν_f$.