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 ${\nu }_f$ of the angular momentum. An expansion in $1/{\nu }_f$ is avoided. Within an additional approximation which adapts the idea of a fixed renormalized \textit{f} level ${\tilde{\epsilon }}_f$, we obtain coupled equations for ${\tilde{\epsilon }}_f$ and the averaged \textit{f} occupation $<n_f>$. These equations resemble to a certain extent those of the usual slave boson mean-field (SB) treatment. In particular, for large ${\nu }_f$ the results for the PRM and the SB approach agree perfectly whereas considerable differences are found for small ${\nu }_f$.

26 pages, 5 figures included, discussion of the DOS added in v2, accepted for publication in Phys. Rev. B