Low energy fixed points of the sigma-tau and the O(3) symmetric Anderson models

TL;DR

This paper investigates the low energy fixed points of sigma-tau and O(3) Anderson models, revealing their Fermi liquid and non-Fermi liquid behaviors, and provides analytical and numerical insights into their excitation spectra and stability.

Contribution

It offers a detailed analysis of the fixed points in these models, including conformal field theory calculations and improved perturbation theory, enhancing understanding of strongly correlated systems.

Findings

Agreement between conformal field theory and NRG results for excitation spectra

Logarithmic corrections make the O(3) Anderson model's interaction marginally stable

The susceptibility to gamma ratio is 8/3, independent of interaction U

Abstract

We study the single channel (compactified) models, the sigma-tau model and the O(3) symmetric Anderson model, which were introduced by Coleman et al., and Coleman and Schofield, as a simplified way to understand the low energy behaviour of the isotropic and anisotropic two channel Kondo systems. These models display both Fermi liquid and marginal Fermi liquid behaviour and an understanding of the nature of their low energy fixed points may give some general insights into the low energy behaviour of other strongly correlated systems. We calculate the excitation spectrum at the non-Fermi liquid fixed point of the sigma-tau model using conformal field theory, and show that the results are in agreement with those obtained in recent numerical renormalization group (NRG) calculations. For the O(3) Anderson model we find further logarithmic corrections in the weak coupling perturbation expansion to those obtained in earlier calculations, such that the renormalized interaction term now becomes marginally stable rather than marginally unstable. We derive a Ward identity and a renormalized form of the perturbation theory that encompasses both the weak and strong coupling regimes and show that the chi/gamma ratio is 8/3 (chi is the total susceptibility, spin plus isospin), independent of the interaction U and in agreement with the NRG calculations.