Metal-insulator transition in cluster dynamical mean field theory: Intersite correlation, cluster size, interaction strength, and the location of the transition line

To gain insight into the physics of the metal-insulator transition and the effectiveness of cluster dynamical mean field theory (DMFT) we have used 1, 2-, and 4-site dynamical mean field theory to solve a polaron model of electrons coupled to a classical phonon field. The metal to polaronic insulator phase boundary is determined along with electron spectral functions and cluster correlation functions. Pronounced cluster size effects occur in the intermediate coupling region in which the cluster calculation leads to a gap and the single-site approximation does not. Differences in spectra (in particular a sharper band edge in the cluster calculation) persist in the strong-coupling regime. A partial density of states is defined encoding a generalized nesting property of the band structure; variations in this density of states account for differences between the dynamical cluster approximation and the cellular-DMFT implementations of cluster DMFT, as well as for differences in behavior between the single-band models appropriate for cuprates and the multiband models appropriate for manganites. A pole or strong resonance in the self-energy is associated with insulating states; the momentum dependence of the pole is found to distinguish between Slater-like and Mott-like mechanisms for metal-insulator transition. Implications for the theoretical treatment of doped manganites are discussed.