Randomly Depleted Kondo Lattices

How is the ``heavy Fermi liquid'' of the Kondo lattice connected to the Kondo impurity ``local Fermi liquid'' as the concentration of f-moments is varied? We study the ensuing interplay of strong correlations and disorder within an $SU(N)$ model in a $N\rightarrow \infty$ limit. Although normal Fermi liquid behavior is well defined close to the two limits of Kondo-lattice and Kondo-impurity, we find that in between them there are strongly in-homogeneous phases with large fractions of quasi-free moments that result in a violation of the usual Fermi-liquid behavior. The full spatial dependence of the mean field solutions allows us to study the depletion driven evolution of inhomogeneities in local quantities like the local susceptibility and the local spectral function in detail. We describe the relevance of our results to recent experiments on $Ce_{1-x}La_{x}CoIn_{5}$.