Analytic continuation from limited noisy Matsubara data

TL;DR

This paper introduces a novel algorithm that reconstructs spectral functions from limited, noisy Matsubara data using interpolation, conformal mapping, and Prony's method, applicable to molecular and condensed matter systems.

Contribution

The paper presents a new algorithm combining interpolation, conformal mapping, and Prony's method for spectral function estimation from limited noisy data.

Findings

Demonstrates effective spectral reconstruction with noisy data

Applicable to both molecular and condensed matter systems

Numerical results validate the algorithm's performance

Abstract

This note proposes a new algorithm for estimating spectral function from limited noisy Matsubara data. We consider both the molecule and condensed matter cases. In each case, the algorithm constructs an interpolant of the Matsubara data and uses conformal mapping and Prony's method to estimate the spectral function. Numerical results are provided to demonstrate the performance of the algorithm.