Equation-of-motion series expansion of double-time Green's functions

Based on the Green's function (GF) equation-of-motion formalism, we develop a method to expand the double-time Green's function into Taylor series of the parameter. in the Hamiltonian H = H-0 + lambda H-1. Here H-0 is the exactly solvable part and H-1 is regarded as the perturbation. To restore the analytical structure of GF, we use the continued fraction to do resummation for the obtained series. The problem of zero-temperature divergence is identified and remedied by the self-consistent series expansion. To demonstrate the implementation of this method, we carry out the weak-as well as the strong-coupling expansion for the Anderson impurity model to order lambda(2). Improved result for the local density of states is obtained by self-consistent second-order strong-coupling expansion and continued fraction resummation.