Benchmark calculations of multiloop pseudofermion fRG

The pseudofermion functional renormalization group (pffRG) is a computational method for determining zero-temperature phase diagrams of frustrated quantum magnets. In recent methodological advance, the commonly employed Katanin truncation flow equations was extended to include multiloop corrections, thereby capturing additional contributions from three-particle vertex [ arXiv:2011.01268 , arXiv:2011.01269 ]. This development has also stimulated significant progress in numerical implementation pffRG, allowing one track evolution vertices under with unprecedented accuracy. However, cutting-edge solvers differ their integration algorithms, heuristics discretize Matsubara frequency grids, and more. To lend confidence robustness state-of-the-art pffRG codes, we present compare results produced two independently developed algorithmically distinct Heisenberg models on three-dimensional lattice geometries. Using cubic (anti)ferromagnet nearest next-nearest neighbor interactions as generic benchmark model, find codes quantitatively agree, often up several orders magnitude digital precision, both level spin-spin correlation functions renormalized fermionic varying loop orders. These calculations further substantiate usage tackle unconventional forms magnetism.