Dynamical Mean Field Theory for Perovskites

Abstract

Using the Hubbard Hamiltonian for transition metal-3d and oxygen-2p states with perovskite geometry, we present a dynamical mean field theory which becomes exactin the limit of large coordination numbers or equivalently large spatial dimensions $D$. The theory is based on a new description of these systems for large $D$ using a selective treatment of different hopping processes which can not be generated by a unique scaling of the hopping element. The model is solved using a perturbational approach and an extended non-crossing approximation. We discuss the breakdown of the perturbation theory near half filling, the origin of the various 3d and 2p bands, the doping dependence of its spectral weight, and the evolution of quasi particles at the Fermi-level upon doping, leading to interesting insight into the dynamical character of the charge carriers near the metal insulator instability of transition metal oxide systems, three dimensional perovskites and other strongly correlated transition metal oxides.