A study of the Kondo Heisenberg model by means of the COM is reported in Ref. [106,107]. In particular the following properties have been computed:
A paramagnetic solution of the model in the context of cuprate oxide superconductors has been derived in Ref.  by considering a two-pole approximation. The effect of spin correlation to the electron energy spectrum has been investigated near the metal-insulator transition.
The ferromagnetic solution has been studied in Ref.  in the context of manganites, where both the intersite antiferromagnetic exchange among localized t electron spins and the strong intra-atomic Hund coupling among the t and e electrons is taken into account. The single- and two- particle Green's functions have been calculated in a fully self-consistent formulation by considering fermionic and bosonic basic composite fields. The study suggests that competing ferromagnetic double-exchange and antiferromagnetic super-exchange interaction lead to a rather nontrivial spin-wave spectrum. While spin excitations have a conventional spectrum in the long-wavelength limit, there is a strong deviation from the spin-wave spectrum of the isotropic Heisenberg model close to the zone boundary. The relevance of the results to the experimental data [108,109,110] has been analyzed.