Comparison of the 1/N expansion and Bethe ansatz results for the degenerate Anderson model

Abstract

The authors find a relation for general N between the conduction band width D of the conventional N-fold-degenerate Anderson model (infinite U) and the cut-off D' imposed on the Bethe ansatz solution of the linear dispersion version of the model. This enables them to compare the results of the 1/N expansion for the ground-state valence n_v and the susceptibility chi with the exact Bethe ansatz results. They find complete agreement to leading and next-leading order in 1/N. The expansion to order 1/N is asymptotically exact as n_v to 0 with chi varies as n_v², and as n_v to 1 with chi varies as exp(1/N(1-n_v)). Numerical comparison shows that the expansion to this order gives almost exact results for N=6 and 8 and excellent results for values of N as low as N=2. The authors find a Wilson number W(N) in complete agreement with their earlier calculations for Coqblin-Schrieffer mode.