LOCAL APPROACH TO THE ONE-BAND HUBBARD-MODEL - EXTENSION OF THE COHERENT-POTENTIAL APPROXIMATION

We present a simple scheme to extend the earlier single-site coherent-potential-approximation (CPA) theories by utilizing connections of the CPA solution with the exact solution of the Falicov-Kimball model in infinite dimensions, and with the single-impurity Anderson-type models. We study the local spectral density of the model at n = I; in the metallic regime, this exhibits a narrow Abrikosov-Suhl resonance and satellite peaks, which correspond, respectively, to the quasiparticle and Hubbard subband structures. This collective resonance disappears in the split-band (insulating) regime, where the CPA is found to be a good approximation. Comparisons are made with numerical works on finite-sized two-dimensional lattices, and good agreement is obtained.