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

TL;DR

This paper applies a projector-based renormalization method to the periodic Anderson model, deriving an effective heavy quasiparticle Hamiltonian that captures heavy Fermion behavior without relying on large degeneracy expansions.

Contribution

The paper introduces an alternative analytical approach to heavy Fermion systems using PRM, avoiding 1/ν_f expansion and providing a new perspective on the model's renormalization.

Findings

PRM yields an effective Hamiltonian with two non-interacting heavy quasiparticle bands.

Results agree with slave boson mean-field for large degeneracy ν_f.

Significant differences between PRM and SB for small ν_f.

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 $\nu_f$.