Spectral Analysis by the Method of Consistent Constraints

TL;DR

This paper introduces a novel spectral analysis method called the method of consistent constraints, which aims to accurately restore spectral density from Matsubara correlators while maintaining smoothness and quantifying deviations.

Contribution

The paper presents a new approach that simultaneously ensures smooth spectral density recovery and provides a measure of deviation from the true spectrum.

Findings

Method produces smooth spectral densities without increasing error bars.

Quantifies deviations from the actual spectral density.

Addresses key challenges in numeric analytic continuation.

Abstract

Two major challenges of numeric analytic continuation---restoring the spectral density, $s(\omega)$, from the corresponding Matsubara correlator, $g(\tau)$---are (i) producing the most smooth/featureless answer for $s(\omega)$ without compromising the error bars on $g(\tau)$ and (ii) quantifying possible deviations of the produced result from the actual answer. We introduce the method of consistent constraints that solves both problems.