Symmetric Anderson impurity model with a narrow band

The single-channel Anderson impurity model is a standard model for the desc ription of magnetic impurities in metallic systems. Usually, the bandwidth represents the largest energy scale of the problem. In this paper, we analy ze the limit of a narrow band, which is relevant for the Mott-Hubbard trans ition in infinite dimensions. For the symmetric model we discuss two differ ent effects. (i) The impurity contribution to the density of states at the Fermi surface always turns out to be negative in such systems. This leads t o a new crossover in the thermodynamic quantities that we investigate using the numerical renormalization group. (ii) Using the Lanczos method, we cal culate the impurity spectral function and demonstrate the breakdown of the skeleton expansion on an intermediate energy scale. Luttinger's theorem, as an example of the local Fermi liquid property of the model, is shown to st ill be valid. [S0163-1829(99)50420-7].