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

Ritz, Nepomuk ; Ge, Anxiang ; Frankenbach, Markus ; Pelz, Mathias ; von Delft, Jan ; Kugler, Fabian B. (2025): Testing the parquet equations and the U(1) Ward identity for real-frequency correlation functions from the multipoint numerical renormalization group. Physical Review Research (7): 033139. ISSN 2643-1564

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.

• Dokumententyp: Artikel (LMU)
• Organisationseinheit (Fakultäten): 17 Physik
• DFG-Fachsystematik der Wissenschaftsbereiche: Naturwissenschaften
• DFG: Gefördert durch die Deutsche Forschungsgemeinschaft (DFG) - 390814868