Advances in lattice hadron physics calculations using the gradient flow

TL;DR

This paper demonstrates that the gradient flow technique enhances the precision and efficiency of lattice hadron physics calculations by improving signal quality, reducing computational effort, and bringing renormalization constants closer to expected values.

Contribution

The study shows that applying the gradient flow to lattice gauge fields improves signal-to-noise ratios, reduces computational costs, and yields more accurate renormalization constants in hadron physics calculations.

Findings

Enhanced signal-to-noise ratio at small flow times

Reduced number of iterations for Wilson-Dirac inverter

Renormalization constants closer to unity

Abstract

Lattice calculations of hadronic observables are aggravated by short-distance fluctuations. The gradient flow, which can be viewed as a particular realisation of the coarse-graining step of momentum space RG transformations, proves a powerful tool for evolving the lattice gauge field to successively longer length scales for any initial coupling. Already at small flow times we find the signal-to-noise ratio of two- and three-point functions significantly enhanced and the projection onto the ground state largely improved, while the effect on the hadronic observables considered here to be negligible. A further benefit is that far fewer conjugate gradient iterations are needed for the Wilson-Dirac inverter to converge. Additionally, we find the renormalisation constants of quark bilinears to be significantly closer to unity.