The soft-gap Anderson model: comparison of renormalization group and local moment approaches

The symmetric Anderson impurity model with a hybridization vanishing at the Fermi level, Delta(1) proportional to \omega\(r), is studied via the numerical renormalization group (NRG) at T = 0; and detailed comparison made with predictions arising from the local moment approach (LMA), a recently developed many-body theory which is found to provide a remarkably successful description of the problem. Results fur the 'normal' (r = 0) impurity model are obtained as a specific case, and likewise compared. Particular emphasis is given both to single-particle excitation dynamics, and to the transition between the strong-coupling (SC) and local moment (LM) phases of the model. Scaling characteristics and asymptotic behaviour of the SC/LM phase boundaries are considered. Single-particle spectra D(omega) are investigated in some detail, for the SC phase in particular. Here, in accordance with a recently established result, the modified spectral functions F(omega) proportional to \omega\(r) D(omega) are found to contain a generalized Kondo resonance that is ubiquitously pinned at the Fermi level; and which exhibits a characteristic low-energy Kondo scale, omega(K)(r), that narrows progressively upon approach to the SC --> LM transition, where it vanishes. Universal scaling of the spectra as the transition is approached thus results. The scaling spectrum characteristic of the normal Anderson model is recovered as a particular case, that exemplifies behaviour characteristic of the SC phase generally, and which is captured quantitatively by the LMA. In all cases the r-dependent scaling spectra are found to possess characteristic low-energy asymptotics, but to he dominated by generalized Doniach-Sunjic tails, in agreement with LMA predictions.