Frithjof Anders (TU Dortmund)
Strongly correlated multi-impurity models: The crossover from a single-impurity problem to lattice models
 
 We present a mapping of correlated multi-impurity Anderson models to a cluster model coupled to a number of effective conduction bands capturing its essential low-energy physics. We can identify the anti-ferromagnetic part of the RKKY interaction and present a mathematical criterion for the number of the effective screening channel, allowing the replacement of the phenomenological exhaustion criterion.
 This provides a distinction between multi-impurity models of first kind and of second kind. For the latter, there are insufficient screening channels available, so that a singlet ground state must be driven by the inter-cluster spin correlations rather then the Kondo physics. 
 We present applications of the theory to the Kondo-hole problem using Wilsons numerical renormalization group as well as cover the emergent coherence, metallic surface states and quantum phase transitions in Kondo insulators. Using an extended Lieb-Mattis theorem provides a deeper understanding on gapped spectra vs finite density of states in particle-hole symmetric situations.