# Disconnected Loop Subtraction Methods in Lattice QCD

## TL;DR

This paper introduces advanced noise subtraction techniques, including matrix deflation and polynomial methods, to improve the efficiency and accuracy of disconnected quark loop calculations in lattice QCD.

## Contribution

It combines deflation with perturbative and polynomial subtraction methods, demonstrating significant noise reduction and computational speed-up in lattice QCD calculations.

## Key findings

- Deflation methods reduce statistical noise in lattice QCD calculations.
- Strong low eigenmode dominance observed at kappa critical.
- Results consistent across quenched and MILC dynamic lattices.

## Abstract

Lattice QCD calculations of disconnected quark loop operators are extremely computer time-consuming to evaluate. To compute these diagrams using lattice techniques, one generally uses stochastic noise methods. These employ a randomly generated set of noise vectors to project out physical signals. In order to strengthen the signal in these calculations, various noise subtraction techniques may be employed. In addition to the standard method of perturbative subtraction, one may also employ matrix deflation techniques using the GMRES-DR and MINRES-DR algorithms as well as polynomial subtraction techniques to reduce statistical uncertainty. Our matrix deflation methods play two roles: they both speed up the solution of the linear equations as well as decrease numerical noise. We show how to combine deflation with either perturbative and polynomial methods to produce extremely powerful noise suppression algorithms. We use a variety of lattices to study the effects. In order to set a benchmark, we first use the Wilson matrix in the quenched approximation. We see strong low eigenmode dominance at kappa critical ($\kappa_{crit}$) in the variance of the vector and scalar operators. We also use MILC dynamic lattices, where we observe deflation subtraction results consistent with the effectiveness seen in the quenched data.