Benchmark Calculations of Multiloop Pseudofermion fRG

TL;DR

This paper benchmarks multiloop pseudofermion functional renormalization group (pffRG) calculations for quantum magnets, demonstrating high numerical consistency between two independent solvers on complex three-dimensional lattice models.

Contribution

It provides the first detailed comparison of two distinct multiloop pffRG solvers, validating their numerical robustness for studying frustrated quantum magnets.

Findings

High agreement between two solvers on spin correlations and vertices

Multiloop pffRG accurately captures complex quantum magnetic behaviors

Benchmark results support broader application of multiloop pffRG methods

Abstract

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