Strongly correlated multi-impurity models: The crossover from a single-impurity problem to lattice models

A mathematical criterion for the number of screening channels in multi-impurity Anderson models is given, dividing these models into two classes. As a consequence, the notion of independent single-ion Kondo effects can be ruled out as the mechanism for a collective singlet formation in heavy-fermion systems. Heavy Fermi liquid formation and its concomitant antiferromagnetic order are linked to an effective hopping between correlated orbitals, whereby the Mott-Hubbard transition in the correlated band provides a microscopic mechanism for the conjectured Lifshitz transition.