KeldyshQFT

A C++ Codebase for real-frequency multiloop functional renormalization group and parquet computations for the single impurity Anderson model

This is the technical documentation for the computational framework designed for the accurate calculation of real-frequency dynamical correlation functions of the single-impurity Anderson model (AM) in the regime of weak to intermediate coupling, see its source code.

It uses quantum field theory within the Keldysh formalism to directly access the self-energy and dynamical susceptibilities along the real-frequency axis, as detailed in this publication. The primary challenge we address is the computationally demanding task of obtaining the full three-dimensional real-frequency dependence of the four-point vertex.

This codebase provides a fully MPI+OpenMP parallelized implementation of the multiloop functional renormalization group, and, independently, the solution of the self-consistent parquet equations within the parquet approximation. It leverages vectorization to handle the additional complexity imposed by the Keldysh formalism, using optimized data structures and highly performant integration routines.

The code itself is written in C++17 and is built using CMake, demanding at least version 3.10. It requires the GSL, boost and Eigen3 libraries as well as the HDF5 library for input and output. For parallelization, the OpenMP and MPI interfaces are used. All these libraries are hence required on the system that is used to build and run the code. Notably, we do not supply precompiled executables, that could be run directly, for several reasons: First, the code makes heavy use of preprocessor flags that must be set before compilation and that are in part used to specify the concrete problem at hand, see Parameters. Second, depending on the system at hand, special compilers for the particular architecture might be available, which could optimize the code during compilation and linking, leading to a significant improvement in performance. The user should hence adapt the file CMakeLists.txt accordingly, such that the required libraries are included and linked properly and all compiler settings are set as desired.

Contents

• Correlation Functions
• Computing diagrams
• Post processing
• I/O
• Miscellaneous
• Parameters
• Algorithms

This technical documentation supplied with the code is generated automatically using the tools Doxygen, Sphinx, Breathe and CMake.

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• Index