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

Abstract

The symmetric Anderson impurity model, with a soft-gap hybridization\nvanishing at the Fermi level with power law r > 0, is studied via the numerical\nrenormalization group (NRG). Detailed comparison is made with predictions\narising from the local moment approach (LMA), a recently developed many-body\ntheory which is found to provide a remarkably successful description of the\nproblem. Results for the `normal' (r = 0) impurity model are obtained as a\nspecific case. Particular emphasis is given both to single-particle excitation\ndynamics, and to the transition between the strong coupling (SC) and local\nmoment (LM) phases of the model. Scaling characteristics and asymptotic\nbehaviour of the SC/LM phase boundaries are considered. Single-particle spectra\nare investigated in some detail, for the SC phase in particular. Here, the\nmodified spectral functions are found to contain a generalized Kondo resonance\nthat is ubiquitously pinned at the Fermi level; and which exhibits a\ncharacteristic low-energy Kondo scale that narrows progressively upon approach\nto the SC->LM transition, where it vanishes. Universal scaling of the spectra\nas the transition is approached thus results. The scaling spectrum\ncharacteristic of the normal Anderson model is recovered as a particular case,\nand is captured quantitatively by the LMA. In all cases the r-dependent scaling\nspectra are found to possess characteristic low-energy asymptotics, but to be\ndominated by generalized Doniach-Sunjic tails, in agreement with LMA\npredictions.\n