Reduced basis methods for the one over N expansion of the Anderson model

he Anderson model simultaneously explains both the bulk properties and valence photoemission spectrum of Cerium and Ytterbium heavy fermion materials. The observed spectral properties of Uranium heavy fermion compounds, however, are qualitatively different; They show a single bandlike peak near the Fermi energy rather than multiple ionization peaks. The spectral properties of Uranium heavy fermion systems represent an unanswered challenge for the description of heavy fermions using the Anderson model.;We investigate this issue using an ;Spin-orbit effects may broaden the low energy peak. We include Hunds first rule splitting for the ;We also make contributions to the formal theory of the 1/N expansion. We present a diagrammatic scheme for classifying the basis elements and their coupling, from which the wave function equations may be directly obtained.;Secondly, we develop a formulation of the 1/N expansion based upon zeroing the ;Finally we undertake a systematic study of the 1/N corrections for the...