Non-Fermi-liquid theory of a compactified Anderson single-impurity model.

We consider a version of the symmetric Anderson impurity model (compactified) which has a non-Fermi-liquid weak-coupling regime. We find that in the Majorana fermion representation the perturbation theory can be conveniently developed in terms of Pfaffian determinants and we use this formalism to calculate the impurity free energy, self-energies, and vertex functions. We derive expressions for the impurity and the local conduction-electron charge and spin-dynamical susceptibilities in terms of the impurity self-energies and vertex functions. In the second-order perturbation theory, a linear temperature dependence of the electrical resistivity is obtained, and the leading corrections to the impurity specific heat are found to behave as {ital T}ln{ital T}. The impurity static susceptibilities have terms in ln{ital T} to zero, first, and second order, and corrections of ln{sup 2}{ital T} to second order as well. The conduction-electron static susceptibilities, and the singlet superconducting paired static susceptibility at the impurity site, have second-order corrections ln{ital T}, which indicate that a singlet conduction-electron pairing resonance forms at the Fermi level (the chemical potential). When the perturbation theory is extended to third order logarithmic divergences are found in the only vertex function {Gamma}{sub 0,1,2,3}(0,0,0,0), which is nonvanishing in the zero-frequency limit. We use the multiplicativemore » renormalization-group (RG) method to sum all the leading-order logarithmic contributions. This gives a weak-coupling low-temperature energy scale {ital T{sub c}}={Delta}exp[-(1/9)({pi}{Delta}/{ital U}){sup 2}], which is the combination of the two independent coupling parameters. The RG scaling equation is derived and shows that the dimensionless coupling constant {bar {ital U}}={ital U}/{pi}{Delta} is increased as the high-energy scale {Delta} is reduced, so our perturbational results can be justified in the regime {ital T}{approx_gt}{ital T{sub c}}.« less