KeldyshQFT: A C++ codebase for real-frequency multiloop functional renormalization group and parquet computations of the single-impurity Anderson model

Nepomuk Ritz, Anxiang Ge, Elias Walter +3 more

arXiv:2405.20996The Journal of Chemical PhysicsAug 7, 20247 citations

Parallel adaptive integration in high-performance functional Renormalization Group computations

Julian Lichtenstein, Jan Winkelmann, David Sánchez de la Peña +2 more

arXiv:1610.09991Oct 31, 20160 citations

arXiv:2311.07667

divERGe implements various Exact Renormalization Group examples

Jonas B. Hauck, Dante Marvin Kennes, Lennart Klebl

Published Nov 13, 2023• 0 citations

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Abstract

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FRG, N-patch FRG, and grid FRG. With this, the divERGe library paves the way for widespread application of FRG as a tool in the study of competing orders in quantum materials.

DOI: 10.18154/rwth-2026-04111

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divERGe implements various Exact Renormalization Group examples

Jonas B. Profe, Dante Marvin Kennes, Lennart Klebl

We present divERGe, an open source, high-performance C/C++/Python library for functional renormalization group (FRG) calculations on lattice fermions. The versatile model interface is tailored to real materials applications and seamlessly integrates with existing, standard tools from the ab-initio community. The code fully supports multi-site, multi-orbital, and non-SU(2) models in all of the three included FRG variants: TU ^2 2 FRG, N-patch FRG, and grid FRG. With this, the divERGe library paves the way for widespread application of FRG as a tool in the study of competing orders in quantum materials.We present divERGe, an open source, high-performance C/C++/Python library for functional renormalization group (FRG) calculations on lattice fermions. The versatile model interface is tailored to real materials applications and seamlessly integrates with existing, standard tools from the ab-initio community. The code fully supports multi-site, multi-orbital, and non-SU(2) models in all of the three included FRG variants: TU ^2 2 FRG, N-patch FRG, and grid FRG. With this, the divERGe library paves the way for widespread application of FRG as a tool in the study of competing orders in quantum materials.

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Codebase release 0.5 for divERGe

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Functional renormalization group for fermion lattice models in three dimensions: Application to the Hubbard model on the cubic lattice

Jannis Ehrlich, Carsten Honerkamp A

The channel-decomposed functional renormalization group (FRG) approach, most recently presented in the variant of truncated-unity FRG (TUFRG), has so far been used for various two-dimensional model systems. Yet for many interesting material systems the third spatial dimension is of clear relevance. Therefore, FRG schemes working in three spatial dimensions (3D) are definitely on the wish list. Here we demonstrate that a 3D TUFRG scheme can be set up in a straightforward extension of previous two-dimensional codes and gives physically sensible results with affordable numerical effort, regarding both the qualitative and quantitative descriptions. The computed phase diagram of the three-dimensional Hubbard model at half filling or perfect nesting shows a phase transition to a $(\ensuremath{\pi},\ensuremath{\pi},\ensuremath{\pi})$-ordered antiferromagnetic ground state for repulsive interactions at an energy scale that compares well with other numerical approaches in the literature. Furthermore, the method allowed us to detect a $d$ -wave pairing and a concurring $(\ensuremath{\pi},\ensuremath{\pi},0)$ antiferromagnetic ground state in the hole-doped Hubbard model.The channel-decomposed functional renormalization group (FRG) approach, most recently presented in the variant of truncated-unity FRG (TUFRG), has so far been used for various two-dimensional model systems. Yet for many interesting material systems the third spatial dimension is of clear relevance. Therefore, FRG schemes working in three spatial dimensions (3D) are definitely on the wish list. Here we demonstrate that a 3D TUFRG scheme can be set up in a straightforward extension of previous two-dimensional codes and gives physically sensible results with affordable numerical effort, regarding both the qualitative and quantitative descriptions. The computed phase diagram of the three-dimensional Hubbard model at half filling or perfect nesting shows a phase transition to a $(\ensuremath{\pi},\ensuremath{\pi},\ensuremath{\pi})$-ordered antiferromagnetic ground state for repulsive interactions at an energy scale that compares well with other numerical approaches in the literature. Furthermore, the method allowed us to detect a $d$-wave pairing and a concurring $(\ensuremath{\pi},\ensuremath{\pi},0)$ antiferromagnetic ground state in the hole-doped Hubbard model.

arXiv:2004.14711Physical review. B./Physical review. BNov 5, 202019 citations

Truncated-Unity Functional Renormalization Group for Multiband Systems With Spin-Orbit Coupling

G. A. H. Schober, Jannis Ehrlich, Timo Reckling +1 more

Although the functional renormalization group (fRG) is by now a well-established method for investigating correlated electron systems, it is still undergoing significant technical and conceptual improvements. In particular, the motivation to optimally exploit the parallelism of modern computing platforms has recently led to the development of the "truncated-unity" functional renormalization group (TU-fRG). Here, we review this fRG variant, and we provide its extension to multiband systems with spin-orbit coupling. Furthermore, we discuss some aspects of the implementation and outline opportunities and challenges ahead for predicting the ground-state ordering and emergent energy scales for a wide class of quantum materials.Although the functional renormalization group (fRG) is by now a well-established method for investigating correlated electron systems, it is still undergoing significant technical and conceptual improvements. In particular, the motivation to optimally exploit the parallelism of modern computing platforms has recently led to the development of the "truncated-unity" functional renormalization group (TU-fRG). Here, we review this fRG variant, and we provide its extension to multiband systems with spin-orbit coupling. Furthermore, we discuss some aspects of the implementation and outline opportunities and challenges ahead for predicting the ground-state ordering and emergent energy scales for a wide class of quantum materials.

arXiv:1710.08830Frontiers in PhysicsMay 8, 201818 citations

KeldyshQFT: A C++ codebase for real-frequency multiloop functional renormalization group and parquet computations of the single-impurity Anderson model

Nepomuk Ritz, Anxiang Ge, Elias Walter +3 more

We provide a detailed exposition of our computational framework designed for the accurate calculation of real-frequency dynamical correlation functions of the single-impurity Anderson model in the regime of weak to intermediate coupling. Using quantum field theory within the Keldysh formalism to directly access the self-energy and dynamical susceptibilities in real frequencies, as detailed in our recent publication [Ge et al., Phys. Rev. B 109, 115128 (2024)], the primary computational challenge is the full three-dimensional real-frequency dependence of the four-point vertex. Our codebase provides a fully MPI+OpenMP parallelized implementation of the functional renormalization group (fRG) and 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. Going beyond the results shown in the previous publication, the code includes functionality to perform fRG calculations in the multiloop framework, up to arbitrary loop order, including self-consistent self-energy iterations. Moreover, implementations of various regulators, such as hybridization, interaction, frequency, and temperature, are supplied.We provide a detailed exposition of our computational framework designed for the accurate calculation of real-frequency dynamical correlation functions of the single-impurity Anderson model in the regime of weak to intermediate coupling. Using quantum field theory within the Keldysh formalism to directly access the self-energy and dynamical susceptibilities in real frequencies, as detailed in our recent publication [Ge et al., Phys. Rev. B 109, 115128 (2024)], the primary computational challenge is the full three-dimensional real-frequency dependence of the four-point vertex. Our codebase provides a fully MPI+OpenMP parallelized implementation of the functional renormalization group (fRG) and 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. Going beyond the results shown in the previous publication, the code includes functionality to perform fRG calculations in the multiloop framework, up to arbitrary loop order, including self-consistent self-energy iterations. Moreover, implementations of various regulators, such as hybridization, interaction, frequency, and temperature, are supplied.

arXiv:2405.20996The Journal of Chemical PhysicsAug 7, 20247 citations

Parallel adaptive integration in high-performance functional Renormalization Group computations

Julian Lichtenstein, Jan Winkelmann, David Sánchez de la Peña +2 more

The conceptual framework provided by the functional Renormalization Group (fRG) has become a formidable tool to study correlated electron systems on lattices which, in turn, provided great insights to our understanding of complex many-body phenomena, such as high- temperature superconductivity or topological states of matter. In this work we present one of the latest realizations of fRG which makes use of an adaptive numerical quadrature scheme specifically tailored to the described fRG scheme. The final result is an increase in performance thanks to improved parallelism and scalability.The conceptual framework provided by the functional Renormalization Group (fRG) has become a formidable tool to study correlated electron systems on lattices which, in turn, provided great insights to our understanding of complex many-body phenomena, such as high- temperature superconductivity or topological states of matter. In this work we present one of the latest realizations of fRG which makes use of an adaptive numerical quadrature scheme specifically tailored to the described fRG scheme. The final result is an increase in performance thanks to improved parallelism and scalability.

arXiv:1610.09991Oct 31, 20160 citations

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FRG, N-patch FRG, and grid FRG. With this, the divERGe library paves the way for widespread application of FRG as a tool in the study of competing orders in quantum materials.

d

-wave pairing and a concurring $(\ensuremath{\pi},\ensuremath{\pi},0)$ antiferromagnetic ground state in the hole-doped Hubbard model.