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International Journal of Modern Physics B

ELECTRON-ELECTRON INTERACTIONS: WARD IDENTITIES

Gerald Dennis Mahan

Published Oct 20, 1992• 7 citations
Publisher

Abstract

We derive several new identities for the correlation functions which are evaluated for electron-electron interactions. These exact results are useful for checking numerous approximations.
DOI
10.1142/s0217979292001493

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Recently, it has become possible to compute real-frequency four-point correlation functions of quantum impurity models using a multipoint extension of the numerical renormalization group (mpNRG). In this work, we perform several numerical consistency checks of the output of mpNRG by investigating exact relations between two- and four-point functions. This includes the Bethe-Salpeter equations and the Schwinger-Dyson equation from the parquet formalism, which we evaluate in two formally identical but numerically nonequivalent ways. We also study the first-order U(1) Ward identity between the vertex and the self-energy for the first time in full generality in the real-frequency Keldysh formalism. We generally find good agreement of all relations, often up to a few percent, both at weak and at strong interaction.