Fourier Accelerated Conjugate Gradient Lattice Gauge Fixing

TL;DR

This paper introduces a Fourier accelerated conjugate gradient method for lattice gauge fixing, significantly improving convergence speed over traditional steepest descent methods.

Contribution

It presents the first implementation of a non-linear conjugate gradient approach with Fourier acceleration for Landau and Coulomb gauge fixing.

Findings

Convergence time reduced by a factor of 2 to 4.

Clear improvement over Fourier accelerated steepest descent.

Effective for high-accuracy gauge fixing.

Abstract

We provide details of the first implementation of a non-linear conjugate gradient method for Landau and Coulomb gauge fixing with Fourier acceleration. 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.