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arXiv · 1507.06407

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

Ning-Hua Tong
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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 $λ$ in the Hamiltonian $H=H_0 + λH_1$. 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 $λ^2$. Improved result for the local density of states is obtained by self-consistent second-order strong-coupling expansion and continued fraction resummation.

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Ning-Hua Tong. 2015-10-30. Equation of Motion Series Expansion of Double Time Green's Functions. https://doi.org/10.1103/physrevb.92.165126

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