SPECTRAL PROPERTIES OF THE ANDERSON IMPURITY MODEL - COMPARISON OF NUMERICAL-RENORMALIZATION-GROUP AND NONCROSSING-APPROXIMATION RESULTS

A comparative study of the numerical-renormalization group and noncros sing-approximation (NCA) results for the spectral functions of the U=i nfinity Anderson impurity model is carried out. The noncrossing approx imation is the simplest conserving approximation and has led to useful insights into strongly correlated models of magnetic impurities. At l ow energies and temperatures the method is known to be inaccurate for dynamical properties due to the appearance of singularities in the phy sical Green's functions. The problems in developing alternative reliab le theories for dynamical properties have made it difficult to quantif y these inaccuracies. In this paper we show, by direct comparison with essentially exact numerical-renormalization-group calculations for th e auxiliary and physical particle spectral functions, that the main so urce of error in the noncrossing approximation is in the lack of verte x corrections in the convolution formulas for physical Green's functio ns. We show that the dynamics of the auxiliary particles within the NC A is essentially correct for a large parameter legion, including the p hysically interesting Kondo regime, for all energy scales down to T-0, the low-energy scale of the model and often well below this scale. De spite the satisfactory description of the auxiliary particle dynamics, the physical spectral functions are not obtained accurately on scales similar to T-0. Our results suggest that self-consistent conserving a pproximations which include vertex terms may provide a highly accurate way of dealing with strongly correlated systems at low temperatures.