Nucleon matrix elements from lattice QCD with all-mode-averaging and a domain-decomposed solver: an exploratory study

TL;DR

This study explores the efficiency of all-mode-averaging combined with a domain-decomposed solver in lattice QCD, demonstrating a twofold reduction in statistical errors for nucleon charge calculations.

Contribution

It introduces an optimized approach for combining AMA with a deflated solver to reduce computational costs in nucleon matrix element computations.

Findings

AMA reduces statistical errors by a factor of two.

Axial charge shows significant excited-state contamination.

Scalar and tensor charges have minimal excited-state contamination.

Abstract

We study the performance of all-mode-averaging (AMA) when used in conjunction with a locally deflated SAP-preconditioned solver, determining how to optimize the local block sizes and number of deflation fields in order to minimize the computational cost for a given level of overall statistical accuracy. We find that AMA enables a reduction of the statistical error on nucleon charges by a factor of around two at the same cost when compared to the standard method. As a demonstration, we compute the axial, scalar and tensor charges of the nucleon in $N_f=2$ lattice QCD with non-perturbatively O(a)-improved Wilson quarks, using O(10,000) measurements to pursue the signal out to source-sink separations of $t_s\sim 1.5$ fm. Our results suggest that the axial charge is suffering from a significant amount (5-10%) of excited-state contamination at source-sink separations of up to $t_s\sim 1.2$ fm, whereas the excited-state contamination in the scalar and tensor charges seems to be small.