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arXiv · 2504.05910

Testing the parquet equations and the U(1) Ward identity for real-frequency correlation functions from the multipoint numerical renormalization group

Nepomuk Ritz·Anxiang Ge·Markus Frankenbach·Mathias Pelz·Jan von Delft·Fabian B. Kugler
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Abstract

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, which we derive 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.

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Nepomuk Ritz, Anxiang Ge, Markus Frankenbach, Mathias Pelz, Jan von Delft, Fabian B. Kugler. 2025-04-08. Testing the parquet equations and the U(1) Ward identity for real-frequency correlation functions from the multipoint numerical renormalization group. https://doi.org/10.1103/3jtq-5wf5

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