Numerical renormalization group for impurity quantum phase transitions: structure ofcritical fixed points

Abstract

The numerical renormalization group method is used to investigate zero-temperature phasetransitions in quantum impurity systems, in particular in the particle–hole symmetricsoft-gap Anderson model. The model displays two stable phases whose fixed points can bebuilt up of non-interacting single-particle states. In contrast, the quantum phase transitionsturn out to be described by interacting fixed points, and their excitations cannot bedescribed in terms of free particles. We show that the structure of the many-bodyspectrum of these critical fixed points can be understood using renormalizedperturbation theory close to certain values of the bath exponents which play the role ofcritical dimensions. Contact is made with perturbative renormalization groupcalculations for the soft-gap Anderson and Kondo models. A complete description ofthe quantum critical many-particle spectra is achieved using suitable marginaloperators; technically this can be understood as epsilon-expansion for full many-bodyspectra.