Degenerate Mass Operator Perturbation Theory in the Hubbard Model

Abstract

The "atomic limit" (kinetic energy zero) of the Hubbard Hamiltonian has extreme degeneracy under very general circumstances. The kinetic energy or hopping term removes this degeneracy. It has been shown by Harris and Lange that there are important first-order manifestations of this fact. For instance, nonlocal correlations exist which invalidate usual Green's function truncation schemes. We present a mass operator perturbation scheme devised on the principle that, first of all, the role of kinetic energy as a breaker of degeneracy must be accounted for. A sort of Taylor's expansion of the mass operator in terms of the kinetic energy is found, the coefficients of which are functionals of the exact Green's functions at zero kinetic energy. The ambiguity due to the degeneracy is removed from these functions self consistently and thereby the degeneracy properly treated. We present a Green's function which accounts for all first-order effects of the kinetic energy.