Interpolative approach for solving the Anderson impurity model

A rational representation for the self-energy is explored to interpolate the solution of the Anderson impurity model in the general orbitally degenerate case. Several constraints such as Friedel's sum rule and the positions of the Hubbard bands, as well as the value of the quasiparticle residue, are used to establish the equations for the coefficients of the interpolation. We employ two fast techniques, the slave-boson mean-field and the Hubbard I approximations, to determine the functional dependence of the coefficients on doping, degeneracy, and the strength of the interaction. The obtained spectral functions and self-energies are in good agreement with the results of the numerically exact quantum Monte Carlo method.