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Numerical analytic continuation of Euclidean data

Authors: 
Ralf-Arno Tripolt, Philipp Gubler, Maksim Ulybyshev, Lorenz von Smekal
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.
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