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.

arXiv comment19 pages, 11 figures

References in corpus (52)

• Exact evolution equation for the effective potential
• The Exact Renormalisation Group and Approximate Solutions
• Functional renormalization group approach to correlated fermion systems
• Topological Mott Insulators
• The nonperturbative functional renormalization group and its applications
• Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions
• Superconductivity and spin-orbit coupling in non-centrosymmetric materials: a review
• Funtional Renormalization Group Study of the Pairing Symmetry and Pairing Mechanism of the FeAs Based High Temperature Superconductors
• A Numerical Renormalization Group Study of the Superconducting and Spin Density Wave Instabilities in MFeAsO${}_{1-x}$F${}_x$ Compounds
• Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice
• Competing many-body instabilities and unconventional superconductivity in graphene
• Density waves and Cooper pairing on the honeycomb lattice
• Functional renormalization group and variational Monte Carlo studies of the electronic instabilities in graphene near 1/4 doping
• Strong Correlations and d+id Superconductivity in Twisted Bilayer Graphene
• Functional Renormalization Group for multi-orbital Fermi Surface Instabilities
• Efficient Parametrization of the Vertex Function, $\Omega$-Scheme, and the (t,t')-Hubbard Model at Van Hove Filling
• Tracking the Footprints of Spin Fluctuations: A MultiMethod, MultiMessenger Study of the Two-Dimensional Hubbard Model
• Ground state and finite temperature signatures of quantum phase transitions in the half-filled Hubbard model on a honeycomb lattice
• The temperature-flow renormalization group and the competition between superconductivity and ferromagnetism
• Renormalization group flows into phases with broken symmetry
• High-performance functional renormalization group calculations for interacting fermions
• Multiloop functional renormalization group for general models
• Multiloop functional renormalization group that sums up all parquet diagrams
• Competing phases of interacting electrons on triangular lattices in moiré heterostructures
• Interaction flow method for many-fermion systems
• Electron-doping versus hole-doping in the 2D t-t' Hubbard model
• Flow of the quasiparticle weight in the N-patch renormalization group scheme
• Truncated Unity Parquet Solver
• Frequency Dependent Vertex Functions of the (t,t')-Hubbard Model at Weak Coupling
• Quantitative functional renormalization-group description of the two-dimensional Hubbard model
• Non-separable frequency dependence of two-particle vertex in interacting fermion systems
• Multiloop functional renormalization group for the two-dimensional Hubbard model: Loop convergence of the response functions
• Competing Orders in two-dimensional Bose-Fermi mixtures
• Antiferromagnetism of the Hubbard Model on a Layered Honeycomb Lattice - Is MgB${}_2$ a Nearly-Antiferromagnetic Metal? -
• Triplet Superconductivity from Nonlocal Coulomb Repulsion in an Atomic Sn Layer Deposited onto a Si(111) Substrate
• Self-energy feedback and frequency-dependent interactions in the functional renormalization group flow for the two-dimensional Hubbard model
• Competing electronic instabilities of extended Hubbard models on the honeycomb lattice: A functional Renormalization Group calculation with high wavevector resolution
• Instabilities on graphene's honeycomb lattice with electron-phonon interactions
• Pseudogap opening in the two-dimensional Hubbard model: A functional renormalization group analysis
• Functional renormalization group for a large moiré unit cell
• Antiferromagnetism and competing charge instabilities of electrons in strained graphene from Coulomb interactions
• Functional Renormalization Group Approach for Inhomogeneous Interacting Fermi-Systems
• Spin-orbit coupled superconductivity: Rashba-Hubbard model on the square lattice
• Electronic instabilities in Penrose quasi-crystals: competition, coexistence and collaboration of order
• Detecting phases in one-dimensional many-fermion systems with the functional renormalization group
• Moiré Engineering of Spin-Orbit Coupling in Twisted Platinum Diselenide
• Electronic Instabilities of the AA-Honeycomb Bilayer
• Competing electronic orders on a heavily doped honeycomb lattice with enhanced exchange coupling
• Functional Renormalization Group Approach for Inhomogeneous One-Dimensional Fermi Systems with Finite-Ranged Interactions
• Effect of exchange interaction on electronic instabilities in the honeycomb lattice: A functional renormalization group study
• Approximating the frequency dependence of the effective interaction in the functional renormalization group for many-fermion systems
• Ferromagnetism and triplet superconductivity in the two-dimensional Hubbard model

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