Conjugate Directions in Lattice Landau and Coulomb Gauge Fixing

TL;DR

This paper enhances lattice gauge fixing algorithms by implementing a conjugate gradient method with Fourier acceleration, significantly reducing convergence time compared to traditional steepest descent methods.

Contribution

It introduces a non-linear conjugate gradient approach with Fourier acceleration for lattice gauge fixing, demonstrating substantial efficiency improvements over existing methods.

Findings

Convergence time reduced by a factor of 2 to 4.

Effective for both logarithmic and common gauge field definitions.

Implementation of an optimal Fourier accelerated steepest descent discussed.

Abstract

We provide details expanding on our implementation of a non-linear conjugate gradient method with Fourier acceleration for lattice Landau and Coulomb gauge fixing. We find clear improvement over the Fourier accelerated steepest descent method, with the average time taken for the algorithm to converge to a fixed, high accuracy, being reduced by a factor of 2 to 4. We show such improvement for the logarithmic definition of the gauge fields here, having already shown this to be the case for a more common definition. We also discuss the implementation of an optimal Fourier accelerated steepest descent method.