A reliable Pade analytical continuation method based on a high accuracy symbolic computation algorithm

TL;DR

This paper introduces a highly accurate symbolic computation algorithm for Pade analytic continuation, improving reliability and precision in reconstructing spectral functions from finite Matsubara frequency data.

Contribution

The paper presents a novel symbolic computation approach that enhances the accuracy of Pade analytic continuation and provides a quantitative reliability test.

Findings

High-accuracy spectral function reconstruction demonstrated.

Error analysis informs reliability testing.

Method applied to Hubbard model Green's functions.

Abstract

We critique a Pade analytic continuation method whereby a rational polynomial function is fit to a set of input points by means of a single matrix inversion. This procedure is accomplished to an extremely high accuracy using a novel symbolic computation algorithm. As an example of this method in action we apply it to the problem of determining the spectral function of a one-particle thermal Green's function known only at a finite number of Matsubara frequencies with two example self energies drawn from the T-matrix theory of the Hubbard model. We present a systematic analysis of the effects of error in the input points on the analytic continuation, and this leads us to propose a procedure to test quantitatively the reliability of the resulting continuation, thus eliminating the black magic label frequently attached to this procedure.