A variational method for spectral functions

TL;DR

This paper introduces a novel frequency-space formulation of the GEVP using the Backus-Gilbert method to analyze Euclidean correlators, enabling improved spectral function extraction in Lattice QCD.

Contribution

It presents a new variational approach in frequency space combining GEVP and Backus-Gilbert methods for spectral analysis in Lattice QCD.

Findings

Successfully applied to NRQCD lattice data

Allows extraction of spectral functions with better frequency resolution

Potential applications in vacuum and finite-temperature physics

Abstract

The Generalized Eigenvalue Problem (GEVP) has been used extensively in the past in order to reliably extract energy levels from time-dependent Euclidean correlators calculated in Lattice QCD. We propose a formulation of the GEVP in frequency space. Our approach consists of applying the model-independent Backus-Gilbert method to a set of Euclidean two-point functions with common quantum numbers. A GEVP analysis in frequency space is then applied to a matrix of estimators that allows us, among other things, to obtain particular linear combinations of the initial set of operators that optimally overlap to different local regions in frequency. We apply this method to lattice data from NRQCD. This approach can be interesting both for vacuum physics as well as for finite-temperature problems.