Coherent potential approximation and projection operators for interacting electrons

A theory of the single-particle excitation spectrum is presented on the basis of the projection operator method combined with the many-body coherent-potential approximation (CPA). The theory describes the dynamics of the excitations by means of an energy-dependent Liouville operator accompanied by a coherent potential which is determined by the self-consistent CPA condition. It is shown that the present theory is essentially equivalent to the dynamical CPA and the dynamical mean-field theory. The Hubbard III approximation and the modified perturbation theory are rederived from the theory. A renormalized perturbation scheme for the Green function is developed on the basis of a general formula for the memory function. It interpolates between the weak- and strong-Coulomb interaction limits, and yields the metal-insulator transition for half-filled bands. Numerical calculations have been performed for the Gutzwiller-Hubbard model on a hypercubic lattice in infinite dimensions. The results show that the theory describes quantitatively the quasiparticle weight vs Coulomb interaction curve, yielding a reasonable critical Coulomb interaction for the metal-insulator transition. It produces the overall features of the excitation spectra and the momentum distributions for various Coulomb interaction strengths.