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Dataset
Open Access
Creative Commons Attribution 4.0 International License
Data for: Testing the parquet equations and the U(1) Ward identity for real-frequency correlation functions from the multipoint numerical renormalization group
Nepomuk Ritz1 , Anxiang Ge1 , Markus Kilian Frankenbach1 , Mathias Pelz1 , Jan von Delft1 , and Fabian B. Kugler1
1Ludwig-Maximilians-Universität München
First published:
April 3, 2025
DOI: 10.57970/at1en-t9f23
Keywords:
dynamical correlation functions
four-point vertex
single-impurity Anderson model
Keldysh formalism
parquet equations
Ward identities
multipoint numerical renormalization group
quantum field theory
correlated electrons
many-body physics

Ritz, N., Ge, A., Frankenbach, M., K., Pelz, M., von Delft, J., and Kugler, F., B. (2025): Data for: Testing the parquet equations and the U(1) Ward identity for real-frequency correlation functions from the multipoint numerical renormalization group. LMU Munich, Faculty of Physics. (Dataset). DOI: 10.57970/at1en-t9f23

wget and curl are the two standard tools that are available on most Linux and macOS computers. wget contains a feature for downloading a list of files: 
wget -x -nH -i 'https://opendata.physik.lmu.de/at1en-t9f23/?list'
curl is missing a feature like that, but the same functionality can be created by combining curl and xargs: 
curl 'https://opendata.physik.lmu.de/at1en-t9f23/?list' | xargs -I URL -n1 bash -c 'curl --create-dirs -o ${1:31} ${1}' -- URL
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 (MuNRG). In this work, we perform several numerical consistency checks of the output of MuNRG 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 non-equivalent 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.
README.md

This dataset contains the data required to reproduce the plots in the related preprint. The directory data/ is split into two datasets, one at weak and one at strong interaction, corresponding the the two different parameter settings studied. Each of those contains:

  • siam_****.h5: This is the vertex as produced by MuNRG, split into all components in such a way that the C++ code (referenced below) can handle it. This data follows the NRG conventions.
  • siam_****_C++.h5: This is the full NRG state, i.e. the collection of self-energy and vertex and read in by the code. This data follows the QFT conventions.
  • Another small .h5 file starting with SIAM. This file holds the self-energy from an independent 2p NRG calculation.
  • The other .h5 files contain the result of an evaluation of the parquet equations or the U(1) WI. Those are needed for the data analysis.
  • The weak interaction dataset additionally contains a converged solution of the parquet equations. This can be used for benchmark purposes.
  • The subdirectory julia/ contains the data produced by Markus Frankenbach for the NRG vertex, using his julia implementation for computing a vertex from NRG partial spectral functions.

The directory scripts/ contains the the ipython notebook plots_for_paper.ipynb used for generating the plots for the paper found in the directory plots/. In addition, the python script arrange_Markus_data.py is used to bring the data from M.F. (in the julia/ subdirectories) into the form of siam_****.h5 required by the code.

Related Code

N. Ritz and A. Ge, KeldyshQFT: A C++ Codebase for real-frequency multiloop functional renormalization group and parquet computations for the single impurity Anderson model, https://github.com/NepomukRitz/KeldyshQFT

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