Equation of Motion Series Expansion of Double Time Green's Functions

Abstract

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 $\lambda$ 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.

21 pages, 7 figures

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• Natural Orbital-Based Lanczos Method for Anderson Impurity Models
• Phase diagram of a pseudogap Anderson model with application to graphene
• Improved strong-coupling perturbation theory of the symmetric Anderson impurity model
• Probing quasiparticle excitations in a doped Mott insulator via Friedel oscillations