We demonstrate that a theoretical framework fully incorporating intra-atomiccorrelations and multiplet structure of the localized 4f states is required inorder to capture the essential physics of rare-earth semiconductors andsemimetals. We focus in particular on the rare-earth semimetal erbium arsenide(ErAs), for which effective one-electron approaches fail to provide aconsistent picture of both high and low-energy electronic states. We treat themany-body states of the Er 4f shell within an atomic approximation in theframework of dynamical mean-field theory. Our results for the magnetic-fielddependence of the 4f local moment, the influence of multiplets on thephotoemission spectrum, and the exchange splitting of the Fermi surface pocketsas measured from Shubnikov-de Haas oscillations, are found to be in goodagreement with experimental results.
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