The Spectral Structure of Correlator Matrices

TL;DR

This paper analyzes the spectral properties of correlator matrices in lattice QCD, focusing on the variational method for extracting excited states, and discusses challenges and alternative approaches with practical lattice data.

Contribution

It provides a detailed examination of the spectral structure of correlator matrices and the variational method, highlighting challenges and exploring alternative spectrum extraction techniques.

Findings

Spectral structure of correlator matrices analyzed

Variational method's effectiveness and limitations discussed

Practical lattice data used to illustrate concepts

Abstract

In lattice QCD spectrum calculations, it is desirable to obtain multiple excited state energies in each symmetry channel. Typically, one constructs several interpolating operators for the symmetry channel of interest, forms the `correlator matrix' of all possible two-point functions, and uses the variational method to obtain as many energy levels as possible. We present a detailed look at this last step, starting from a discussion of the symmetry properties and spectral structure of the correlator matrix. We continue by motivating and describing the variational method, before discussing some conceptual and practical challenges concerning the light baryon sector. We conclude by mentioning some alternate spectrum extraction methods currently under study. Throughout, we attempt to quantify all approximations and assumptions, and we illustrate our points using a nucleon correlator matrix estimated on dynamical two-flavor lattice data.