Analytic continuation with Padé decomposition

Abstract

The ill-posed analytic continuation problem for Green's functions or self-energies can be done using the Padé rational polynomial approximation. However, to extract accurate results from this approximation, high precision input data of the Matsubara Green's function are needed. The calculation of the Matsubara Green's function generally involves a Matsubara frequency summation which cannot be evaluated analytically. Numerical summation is requisite but it converges slowly with the increase of the Matsubara frequency. Here we show that this slow convergence problem can be significantly improved by utilizing the Padé decomposition approach to replace the Matsubara frequency summation by a Padé frequency summation, and high precision input data can be obtained to successfully perform the Padé analytic continuation.

4 pages, 3 figures

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• Learned Optimizers for Analytic Continuation
• Minimal Pole Representation and Controlled Analytic Continuation of Matsubara Response Functions
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• Strong Boundary and Trap Potential Effects on Emergent Physics in Ultra-Cold Fermionic Gases