Reference results for the momentum space functional renormalization group

TL;DR

This paper provides a comprehensive set of benchmark results for the functional renormalization group method, aiming to standardize and verify implementations through reproducibility and comparison.

Contribution

It offers detailed implementation data and reproducible results across multiple independent FRG codes, establishing a reference standard for the community.

Findings

Reproducibility of FRG results across implementations

Comparison with literature results confirms accuracy

Proposes a shared benchmark set for future FRG studies

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.