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Data for: Real-frequency quantum field theory applied to the single-impurity Anderson model
Anxiang Ge1, Nepomuk Ritz1, Elias Walter1, Santiago Aguirre1, Jan von Delft1, and Fabian Kugler2
1Ludwig-Maximilians-Universität München
2Center for Computational Quantum Physics, Flatiron Institute, New York, USA
First published:
Aug. 24, 2023
DOI: 10.57970/xeqvs-w3p49
Keywords:
dynamical correlation functions
four-point vertex
single-impurity Anderson model
Keldysh formalism
functional renormalization group
parquet equations
parquet approximation
numerical renormalization group
quantum field theory
correlated electrons
many-body physics

Ge, A., Ritz, N., Walter, E., Aguirre, S., von Delft, J., and Kugler, F. (2023): Data for: Real-frequency quantum field theory applied to the single-impurity Anderson model. LMU Munich, Faculty of Physics. (Dataset). DOI: 10.57970/xeqvs-w3p49

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/xeqvs-w3p49/?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/xeqvs-w3p49/?list' | xargs -I URL -n1 bash -c 'curl --create-dirs -o ${1:31} ${1}' -- URL
Abstract
A major challenge in the field of correlated electrons is the computation of dynamical correlation functions. For comparisons with experiment, one is interested in their real-frequency dependence. This is difficult to compute, as imaginary-frequency data from the Matsubara formalism require analytic continuation, a numerically ill-posed problem. Here, we apply quantum field theory to the single-impurity Anderson model (AM), using the Keldysh instead of the Matsubara formalism with direct access to the self-energy and dynamical susceptibilities on the real-frequency axis. We present results from the functional renormalization group (fRG) at one-loop level and from solving the self-consistent parquet equations in the parquet approximation. In contrast to previous Keldysh fRG works, we employ a parametrization of the four-point vertex which captures its full dependence on three real-frequency arguments. We compare our results to benchmark data obtained with the numerical renormalization group and to second-order perturbation theory. We find that capturing the full frequency dependence of the four-point vertex significantly improves the fRG results compared to previous implementations, and that solving the parquet equations yields the best agreement with the NRG benchmark data, but is only feasible up to moderate interaction strengths. Our methodical advances pave the way for treating more complicated models in the future.
README.md

Contact: nepomuk.ritz@physik.uni-muenchen.de

This dataset contains the data required to reproduce the plots in the related preprint. The directory data/ includes the raw data, in .hdf5 format, for the two-point functions from fRG, PA, K1SF, PT2 and NRG computations needed to extract the response functions studied in the paper, as well as data for the two-particle (i.e. four-point) vertex. The NRG data for the four-point vertex are provided in .mat and .npy format.

The notebook data_analysis.ipynb together with the module data_container.py provides all details, including the full data analysis and the plotting scripts to reproduce the plots, which themselves can be found in the directory plots/.

Related preprint

Anxiang Ge, Nepomuk Ritz, Elias Walter, Santiago Aguirre, Jan von Delft and Fabian B. Kugler, Real-frequency quantum field theory applied to the single-impurity Anderson model, arXiv:2307.10791, https://doi.org/10.48550/arXiv.2307.10791

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