Beyond Generalized Eigenvalues in Lattice Quantum Field Theory

TL;DR

This paper introduces a new framework combining the generalized eigenvalue method and Prony's method for analyzing correlation functions in lattice quantum field theory, leveraging matrix polynomials to improve spectral analysis.

Contribution

It develops a unified algebraic approach that integrates the strengths of GEM and PM, enhancing spectral information extraction from noisy data in lattice QFT.

Findings

Combines GEM and PM into a matrix polynomial framework.

Enhances spectral analysis of correlation functions.

Suggests pairing with Bayesian model averaging for optimal results.

Abstract

Two analysis techniques, the generalized eigenvalue method (GEM) or Prony's (or related) method (PM), are commonly used to analyze statistical estimates of correlation functions produced in lattice quantum field theory calculations. GEM takes full advantage of the matrix structure of correlation functions but only considers individual pairs of time separations when much more data exists. PM can be applied to many time separations and many individual matrix elements simultaneously but does not fully exploit the matrix structure of the correlation function. We combine both these methods into a single framework based on matrix polynomials. As these algebraic methods are well known for producing extensive spectral information about statistically-noisy data, the method should be paired with some information criteria, like the recently proposed Bayesean model averaging.