A functional renormalization group approach to the Anderson impurity model

Abstract

We develop a functional renormalization group approach which describes the low-energysingle-particle properties of the Anderson impurity model up to intermediate on-siteinteractions , where Δ is the hybridization in the wide-band limit. Our method is based on a generalization of amethod proposed by Schütz et al (2005 Phys. Rev. B 72 035107), using two independentHubbard–Stratonovich fields associated with transverse and longitudinal spin fluctuations.Although we do not reproduce the exponentially small Kondo scale in the limit , the spin fluctuations included in our approach remove theunphysical Stoner instability predicted by mean field theory forU>πΔ. We discuss different decoupling schemes and show that a decoupling which manifestlyrespects the spin-rotational invariance of the problem gives rise to the lowest quasiparticleweight. To obtain a closed flow equation for the fermionic self-energy we also propose a newscheme of truncation of the functional renormalization group flow equations usingDyson–Schwinger equations to express bosonic vertex functions in terms of fermionic ones.