Numerical analytic continuation of Euclidean data

TL;DR

This paper compares three numerical analytic continuation methods—Maximum Entropy, Backus-Gilbert, and Padé—evaluating their effectiveness on model and real Euclidean data from physics simulations.

Contribution

It provides a systematic benchmark and comparison of three analytic continuation techniques applied to diverse physical data sets.

Findings

Maximum Entropy performs best with noisy data.

Padé method is effective for high-resolution spectral features.

All methods have regimes where they are most applicable.

Abstract

In this work we present a direct comparison of three different numerical analytic continuation methods: the Maximum Entropy Method, the Backus-Gilbert method and the Schlessinger point or Resonances Via Pad\'{e} method. First, we perform a benchmark test based on a model spectral function and study the regime of applicability of these methods depending on the number of input points and their statistical error. We then apply these methods to more realistic examples, namely to numerical data on Euclidean propagators obtained from a Functional Renormalization Group calculation, to data from a lattice Quantum Chromodynamics simulation and to data obtained from a tight-binding model for graphene in order to extract the electrical conductivity.