Spectral Densities of Response Functions for the O(3) Symmetric Anderson and Two Channel Kondo Models

TL;DR

This paper investigates the spectral properties of the O(3) symmetric Anderson and two channel Kondo models, revealing how response functions behave near different fixed points and interpreting results via Majorana fermions.

Contribution

It establishes the exact equivalence between the Anderson and two channel Kondo models using conformal field theory and computes response functions with NRG, providing new insights into their low-energy excitations.

Findings

Spectral densities show |omega| dependence at the marginal Fermi liquid fixed point.

Zero Majorana mode exhibits a delta function contribution, decreasing exponentially with U.

Dynamical spin susceptibility exhibits a ln omega divergence at low frequencies.

Abstract

The O(3) symmetric Anderson model is an example of a system which has a stable low energy marginal Fermi liquid fixed point for a certain choice of parameters. It is also exactly equivalent, in the large U limit, to a localized model which describes the spin degrees of freedom of the linear dispersion two channel Kondo model. We first use an argument based on conformal field theory to establish this precise equivalence with the two channel model. We then use the numerical renormalization group (NRG) approach to calculate both one-electron and two-electron response functions for a range of values of the interaction strength U. We compare the behaviours about the marginal Fermi liquid and Fermi liquid fixed points and interpret the results in terms of a renormalized Majorana fermion picture of the elementary excitations. In the marginal Fermi liquid case the spectral densities of all the Majorana fermion modes display a |omega| dependence on the lowest energy scale, and in addition the zero Majorana mode has a delta function contribution. The weight of this delta function is studied as a function of the interaction U and is found to decrease exponentially with U for large U. Using the equivalence with the two channel Kondo model in the large U limit, we deduce the dynamical spin susceptibility of the two channel Kondo model over the full frequency range. We use renormalized perturbation theory to interpret the results and to calculate the coefficient of the ln omega divergence found in the low frequency behaviour of the T=0 dynamic susceptibility.