Application of Laplace filters to the analysis of lattice time correlators

TL;DR

This paper introduces regulated Laplace filters for lattice correlation data analysis, effectively reducing covariance matrix ill-conditioning and excited-state contamination, thereby improving the extraction of physical information from lattice simulations.

Contribution

The paper presents a novel application of regulated Laplace filters to address covariance matrix issues and excited-state contamination in lattice correlation functions.

Findings

Laplace filters significantly reduce covariance matrix condition numbers.

Filters can suppress excited-state contamination in matrix element calculations.

Potential to develop new spectral analysis methods for lattice data.

Abstract

The analysis of lattice simulation correlation function data is notoriously hindered by the ill-conditioning of the Euclidean time covariance matrix. Additionally, the isolation of a single physical state in such functions is generally affected by systematic contamination from unwanted states. In this paper, we present a new methodology based on regulated Laplace filters and demonstrate that it can be used to address both issues using state-of-the-art simulation data. Regulated Laplace filters are invertible high-pass filters that suppress local correlations in the data, and we show that they can reduce the condition number of covariance matrices by several orders of magnitude. Furthermore, Laplace filters can annihilate functions that decay exponentially with time, which can be used to alter the spectrum of a lattice correlation function. We show that this property can be exploited to significantly reduce excited-state contamination in the determination of matrix elements. The same property can also be used to constrain the spectral content of a correlation function and has the potential to form the basis of new methods to extract physical information from lattice data.