Mixed valence as an almost broken symmetry

By using a generalized version of the infinite-$U$ Anderson model, strong-coupling properties of mixed-valence systems are modeled by means of an expansion about a broken-symmetry mean-field theory. A renormalized Fermi liquid, with heavy-fermion bands in the lattice is an intrinsic feature of this mean-field theory. Strong-coupling divergence of the Kondo coupling constant arises as a direct consequence of the zero-mode fluctuations about the broken-symmetry state. In the large-degeneracy limit these fluctuations vanish and the broken-symmetry state is an exact solution, explicitly confirmed for the single-impurity case by a new Bethe-ansatz solution. The crossover to strong coupling is a vestige of the phase transition into the broken-symmetry state. Landau parameters, charge and spin correlations of the heavy Fermi liquid are directly related to the fluctuations about the broken-symmetry state. The general approach presented is applicable to an arbitrary number of impurities or a lattice. Analytic results are presented for the Landau parameters, the dynamical charge and spin correlations in the one- and the two-impurity models, and the one-impurity $f$ spectral function.