We demonstrate that a theoretical framework fully incorporating intra-atomic correlations and multiplet structure of the localized 4f states is required in order to capture the essential physics of rare-earth semiconductors and semimetals. We focus i
n particular on the rare-earth semimetal erbium arsenide (ErAs), for which effective one-electron approaches fail to provide a consistent picture of both high and low-energy electronic states. We treat the many-body states of the Er 4f shell within an atomic approximation in the framework of dynamical mean-field theory. Our results for the magnetic-field dependence of the 4f local moment, the influence of multiplets on the photoemission spectrum, and the exchange splitting of the Fermi surface pockets as measured from Shubnikov-de Haas oscillations, are found to be in good agreement with experimental results.
