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

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.

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Publication Details

Journal
Physical Review Research
Published
2025-06-16
DOI
https://doi.org/10.1103/3jtq-5wf5
Citations
3
Primary Topic
Image and Signal Denoising Methods
Type
article
Field-Weighted Citation Impact
3.83

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article

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

Anxiang Ge, Jan von Delft, Mathias Pelz, Fabian B. Kugler et al.
3 citations
Physical Review Research
Image and Signal Denoising Methods
3.83
article

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

Anxiang Ge, Jan von Delft, Mathias Pelz, Fabian B. Kugler, Markus Frankenbach, Karl J. Friston
article en
3 citations

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 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.

Physical Review ResearchVol. 7(3)
University of Cologne (DE), Flatiron Health (United States) (US), Flatiron Institute (US), Ludwig-Maximilians-Universität München (DE)
International Max Planck Research School for Environmental, Cellular and Molecular Microbiology, Flatiron Health, Deutsche Forschungsgemeinschaft, Studienstiftung des Deutschen Volkes, International Max Planck Research School for Advanced Methods in Process and Systems Engineering, Gauss Centre for Supercomputing, International Max Planck Research School for Quantum Science and Technology, Leibniz-Gemeinschaft, Leibniz-Rechenzentrum
Openalex Percentile: Top 6%
Image and Signal Denoising Methods
3.83
DOIOpen Access PDFOpenAlex
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