mpNRG PSFs used in: "Computing and compressing local vertex functions in imaginary and real frequencies from the multipoint numerical renormalization group using quantics tensor cross interpolation"

Citation: Frankenbach, Markus and Pelz, Mathias and Ritter, Marc and Ritz, Nepomuk and von Delft, Jan and Ge, Anxiang and Shim, Jeongmin: mpNRG PSFs used in: "Computing and compressing local vertex functions in imaginary and real frequencies from the multipoint numerical renormalization group using quantics tensor cross interpolation". May 2025. Open Data LMU. 10.5282/ubm/data.613

Abstract

The multipoint numerical renormalization group (mpNRG) is a powerful impurity solver that provides accurate spectral data useful for computing local, dynamic correlation functions in imaginary or real frequencies non-perturbatively across a wide range of interactions and temperatures. It gives access to a local, non-perturbative four-point vertex in imaginary and real frequencies, which can be used as input for subsequent computations such as diagrammatic extensions of dynamical mean field theory. However, computing and manipulating the real-frequency four-point vertex on large, dense grids quickly becomes numerically challenging when the density and/or the extent of the frequency grid is increased. In this paper, we compute four-point vertices in a strongly compressed quantics tensor train format using quantics tensor cross interpolation, starting from discrete partial spectral functions obtained from mpNRG. This enables evaluations of the vertex on frequency grids with resolutions far beyond the reach of previous implementations. We benchmark this approach on the four-point vertex of the single-impurity Anderson model across a wide range of physical parameters, both in its full form and its asymptotic decomposition. For imaginary frequencies, the full vertex can be represented to an accuracy of 10−3 with maximum bond dimensions not exceeding 120. The more complex full real-frequency vertex requires maximum bond dimensions not exceeding 170 for 1% accuracy. Our work marks another step toward tensor-train-based diagrammatic calculations for correlated electronic lattice models starting from a local, non-perturbative mpNRG vertex.

Uncontrolled Keywords

multipoint numerical renormalization group, Keldyh vertex, Matsubara vertex, tensor cross interpolation, correlated electrons, symmetric estimators

• Item Type: Data
• Contact Person: Frankenbach, Markus
• E-Mail of Contact: m.frankenbach at physik.uni-muenchen.de
• Subjects: Physics
• Dewey Decimal Classification: 500 Natural sciences and mathematics; 500 Natural sciences and mathematics > 530 Physics