Reconstructing lattice QCD spectral functions with stochastic pole expansion and Nevanlinna analytic continuation

TL;DR

This paper compares two analytic continuation methods, stochastic pole expansion and Nevanlinna, for reconstructing spectral functions from lattice QCD data, highlighting the robustness of the former and the instability of the latter.

Contribution

It provides a comprehensive evaluation of stochastic pole expansion and Nevanlinna methods on mock lattice QCD data, revealing their strengths and limitations.

Findings

Stochastic pole expansion accurately recovers spectral features.

Nevanlinna method shows numerical instability and spurious peaks.

Stochastic method is resilient to input noise.

Abstract

The reconstruction of spectral functions from Euclidean correlation functions is a well-known, yet ill-posed inverse problem in the fields of many-body and high-energy physics. In this paper, we present a comprehensive investigation of two recently developed analytic continuation methods, namely stochastic pole expansion and Nevanlinna analytic continuation, for extracting spectral functions from mock lattice QCD data. We examine a range of Euclidean correlation functions generated by representative models, including the Breit-Wigner model, the Gaussian mixture model, the resonance-continuum model, and the bottomonium model. Our findings demonstrate that the stochastic pole expansion method, when combined with the constrained sampling algorithm and the self-adaptive sampling algorithm, successfully recovers the essential features of the spectral functions and exhibits excellent resilience to noise of input data. In contrast, the Nevanlinna analytic continuation method suffers from numerical instability, often resulting in the emergence of spurious peaks and significant oscillations in the high-energy regions of the spectral functions, even with the application of the Hardy basis function optimization algorithm.