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

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.

Comments: 10 pages, 6 figures, we provide an additional document with code examples and the data to reproduce the results, corrected a mistake in the remark on systematics from unresolved states without influence on the results of the paper