Improved Smoothing Algorithms for Lattice Gauge Theory

TL;DR

This paper compares the effectiveness of various gauge field smoothing algorithms, including an improved APE smearing, on lattice configurations at different spacings, providing calibration formulas for their relative smoothing rates.

Contribution

It introduces an improved version of APE smearing and evaluates its performance relative to other algorithms on improved lattice configurations.

Findings

Improved algorithms show clear benefits at coarse lattice spacing.

At fine lattice spacing, algorithms perform similarly, enabling quantitative calibration.

Calibration formulas accurately describe smoothing rates at a microscopic level.

Abstract

The relative smoothing rates of various gauge field smoothing algorithms are investigated on ${\cal O}(a^2)$-improved $\suthree$ Yang--Mills gauge field configurations. In particular, an ${\cal O}(a^2)$-improved version of APE smearing is motivated by considerations of smeared link projection and cooling. The extent to which the established benefits of improved cooling carry over to improved smearing is critically examined. We consider representative gauge field configurations generated with an ${\cal O}(a^2)$-improved gauge field action on $\1$ lattices at $\beta=4.38$ and $\2$ lattices at $\beta=5.00$ having lattice spacings of 0.165(2) fm and 0.077(1) fm respectively. While the merits of improved algorithms are clearly displayed for the coarse lattice spacing, the fine lattice results put the various algorithms on a more equal footing and allow a quantitative calibration of the smoothing rates for the various algorithms. We find the relative rate of variation in the action may be succinctly described in terms of simple calibration formulae which accurately describe the relative smoothness of the gauge field configurations at a microscopic level.