Real-space renormalization group study of the Anderson impurity model

Abstract

In this thesis, we present a real-space renormalization group study of the Anderson impurity model(AIM) that describes itinerant fermions hybridized with an impurity. We use the quantum renormalization group method to map the exact RG equation to a path integral of the dynamical hopping and hybridization fields. We solve the saddle-point equation of the bulk theory that governs the fluctuating renormalization group flow, which becomes exact in the large $N$ limit. From the solution, we show that the ranges of the renormalized hopping and hybridization are determined by the energy gap of the system. When the system is at the critical point, those ranges increase indefinitely both in the spatial and temporal directions as the RG scale increases.