Error estimates and specification parameters for functional renormalization

TL;DR

This paper introduces a method to estimate errors in truncated functional renormalization group equations by analyzing how different truncation specifications affect results, demonstrated on the BCS-BEC crossover.

Contribution

It proposes a strategy to quantify errors in functional renormalization group truncations using specification parameters, highlighting the impact of truncation choices.

Findings

Specification parameters can quantify the error in truncations.

Frequency dependence affects the accuracy of results.

Shortcomings of frequency independent cutoff functions are identified.

Abstract

We present a strategy for estimating the error of truncated functional flow equations. While the basic functional renormalization group equation is exact, approximated solutions by means of truncations do not only depend on the choice of the retained information, but also on the precise definition of the truncation. Therefore, results depend on specification parameters that can be used to quantify the error of a given truncation. We demonstrate this for the BCS-BEC crossover in ultracold atoms. Within a simple truncation the precise definition of the frequency dependence of the truncated propagator affects the results, indicating a shortcoming of the choice of a frequency independent cutoff function.