Numerical Renormalization Group for Impurity Quantum Phase Transitions: Structure of Critical Fixed Points

TL;DR

This paper uses the numerical renormalization group to analyze quantum impurity phase transitions, revealing that critical fixed points involve interacting many-body states and can be understood through renormalized perturbation theory near critical bath exponents.

Contribution

It provides a detailed analysis of the structure of critical fixed points in impurity quantum phase transitions, connecting numerical results with perturbative renormalization group theory.

Findings

Critical fixed points are interacting, not free-particle states.

Many-body spectra at criticality can be described using epsilon-expansion techniques.

The structure of spectra is understood via renormalized perturbation theory near critical bath exponents.

Abstract

The numerical renormalization group method is used to investigate zero temperature phase transitions in quantum impurity systems, in particular in the particle-hole symmetric soft-gap Anderson model. The model displays two stable phases whose fixed points can be built up of non-interacting single-particle states. In contrast, the quantum phase transitions turn out to be described by interacting fixed points, and their excitations cannot be described in terms of free particles. We show that the structure of the many-body spectrum of these critical fixed points can be understood using renormalized perturbation theory close to certain values of the bath exponents which play the role of critical dimensions. Contact is made with perturbative renormalization group calculations for the soft-gap Anderson and Kondo models. A complete description of the quantum critical many-particle spectra is achieved using suitable marginal operators; technically this can be understood as epsilon-expansion for full many-body spectra.