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arXiv:cond-mat/0106458 · Physical review. B, Condensed matter

Quantum phase transitions in models of coupled magnetic impurities

Matthias Vojta C, R. Bulla, Walter Hofstetter

Published Apr 1, 2002• 122 citations
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Abstract

We discuss models of interacting magnetic impurities coupled to a metallic host, which show one or more boundary quantum phase transitions where the ground-state spin changes as a function of the interimpurity couplings. The simplest example is realized by two spin-$\frac{1}{2}$ Kondo impurities coupled to a single orbital of the host. We investigate the phase diagram and crossover behavior of this model and present numerical renormalization-group results together with general arguments showing that the singlet-doublet quantum phase transition is either of first order or of the Kosterlitz-Thouless type, depending on the symmetry of the Kondo couplings. Thus we find an exponentially small energy scale within the Kondo regime, and a two-stage Kondo effect, in a single-channel situation. Connections to other models and possible applications are discussed.

DOI
10.1103/physrevb.65.140405

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