Single-particle spectrum for a model of fermions interacting with   two-level local excitations on a lattice: A dynamical CPA approach
  The problem of motion of a single electron interacting with a periodic lattice of two-level systems is investigated within a spinless fermion model. The Green's function is calculated in a single-site dynamical coherent potential approximation which is equivalent to DMFT. The picture of one-electron density of states is obtained for various values of the tunnel splitting and coupling between the electron and two-level system. The occurrence of a band splitting with increase of the coupling is demonstrated. 
A. O. Anokhin, A. V. Zarubin and V. Yu. Irkhin