Reference results for the momentum space functional renormalization group

Abstract

The functional renormalization group (FRG), an established computational method for quantum many-body phenomena, has been subject to a diversification in topical applications, analytic approximations and numerical implementations. Despite significant efforts to accomplish a coherent standard through benchmarks and the reproduction of previous results, no systematic and comprehensive comparison has been provided until now. While this has not prevented the publication of relevant scientific results we argue that established mutual agreement across realizations will strengthen confidence in the method. To this end we report explicit implementational details and numerical data reproduced thrice in independent FRG implementations up to machine accuracy. To substantiate the reproducibility of our calculations we scrutinize pillar FRG results reported in the literature, and discuss our calculations of these reference systems. We mean to entice other groups to reproduce and establish this set of benchmark FRG results thus propagating the joint effort of the FRG community to engage in a shared knowledge repository as a reference standard for FRG implementations.

19 pages, 11 figures

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Cited by in corpus (25)

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• TU${}^2$FRG -- a scalable approach for truncated unity functional renormalization group in generic fermionic models
• Rashba spin-orbit coupling in the square lattice Hubbard model: A truncated-unity functional renormalization group study
• The kagome Hubbard model from a functional renormalization group perspective
• Sublattice modulated superconductivity in the Kagome Hubbard model
• divERGe implements various Exact Renormalization Group examples
• Theory of intervalley-coherent AFM order and topological superconductivity in tWSe${}_2$
• Superconductivity of repulsive spinless fermions with sublattice potentials
• Spin and pair density waves in 2D altermagnetic metals
• Competition between d-wave superconductivity and magnetism in uniaxially strained Sr2RuO4
• Hybrid s-wave superconductivity in CrB${}_2$
• Better Integrators for Functional Renormalization Group Calculations
• Magic angle of Sr${}_2$RuO${}_4$: Optimizing correlation-driven superconductivity
• Loop Current Order on the Kagome Lattice
• Consistent combination of truncated-unity functional renormalization group and mean-field theory
• Quantum spin Hall insulator on the honeycomb lattice induced by ferromagnetic exchange interaction
• Chern number landscape of spin-orbit coupled chiral superconductors
• Incommensurate magnetic order: A fingerprint for electronic correlations in hole-doped cuprates
• Fractionalized Superconductivity Mediated by Majorana Fermions in the Kitaev-Kondo Lattice
• Kekulé order from diffuse nesting near higher-order Van Hove points
• Van-Hove tuning of Fermi surface instabilities through compensated metallicity
• Surface Functional Renormalization Group for Layered Quantum Materials
• Theory of unconventional magnetism in a Cu-based kagome metal
• Competing instabilities of the extended Hubbard model on the triangular lattice: Truncated-unity functional renormalization group and application to moiré materials
• Spin bond order driven by extended repulsive interactions in doped graphene