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

K. S. D. Beach·R. J. Gooding·F. Marsiglio
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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.

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K. S. D. Beach, R. J. Gooding, F. Marsiglio. 1999-11-23. A reliable Pade analytical continuation method based on a high accuracy symbolic computation algorithm. https://doi.org/10.1103/physrevb.61.5147

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