On the equivalence of Prony and Lanczos methods for Euclidean correlation functions

TL;DR

This paper demonstrates the analytical equivalence of the oblique Lanczos method and Prony's method for analyzing Euclidean correlators, highlighting their advantages over traditional approaches despite not solving the signal-to-noise issue.

Contribution

It establishes the equivalence between the oblique Lanczos method and Prony's Generalised Eigenvalue Method for Euclidean correlator analysis.

Findings

Oblique Lanczos and Prony methods are analytically equivalent.

Both methods outperform the standard effective mass approach.

Signal-to-noise problem remains unsolved by these methods.

Abstract

We investigate the oblique Lanczos method recently put forward in arXiv:2406.20009 for analysing Euclidean correlators in lattice field theories and show that it is analytically equivalent to the well known Prony Generalised Eigenvalue Method (PGEVM). Moreover, we discuss that the signal-to-noise problem is not aleviated by either of these two methods. Still, both methods show clear advantages when compared to the standard effective mass approach.