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.
The impurity Green function and dynamical susceptibilities for the two-channel Anderson impurity model are calculated. An exact expression for the self-energy of the impurity Green function as ratio of two correlation functions is given. The imaginary part of the self-energy scales as $\sqrt{\ensuremath{\mid}\ensuremath{\omega}∕{T}_{K}\ensuremath{\mid}}$ for $T\ensuremath{\rightarrow}0$, serving as a hallmark for non-Fermi behavior. The many-body resonance is pinned to a universal value of $1∕(2\ensuremath{\pi}\ensuremath{\Delta})$ at $\ensuremath{\omega}=0$ for arbitrary local occupation in contrary to the single-channel Anderson impurity model. Its shape becomes increasingly more symmetric for the Kondo regimes of the model. The dynamical spin and channel susceptibilities are governed by two energy scales
TK and
Th, and their ${\ensuremath{\chi}}^{\ensuremath{''}}(\ensuremath{\omega})$ approach a constant value for $\ensuremath{\omega}\ensuremath{\rightarrow}0$.
The local Cu-O model is a local version of the extended Hubbard model and corresponds to a two-channel Anderson impurity model in which the two channels correspond to screening and hybridizing channels, respectively, and the screening interaction,
Udc, is short range. The model represents a more realistic model for the local excitations in heavy fermions and may also be of relevance in understanding the normal state properties of high temperature superconductors. Below a critical screening strength,
UdcUdccrit the particle-hole symmetric model exhibits Fermi-liquid behavior, whereas for
Udc>
Udccrit a non-Fermi-liquid state forms. Here, we report results of a numerical renormalization group calculation for the spectral density of single-particle excitations, in both the Fermi-liquid and non-Fermi-liquid regimes. The Kondo resonance is strongly modified for
Udc close to
Udccrit and is destroyed for
Udc>
Udccrit. The relevance of these results for high temperature superconductors and the photoemission spectra of heavy fermions is discussed.