Gauge-Fixed Fourier Acceleration

TL;DR

This paper introduces a gauge-fixed Fourier acceleration method within a hybrid Monte Carlo algorithm to reduce critical slowing down in lattice gauge theories, demonstrating preliminary improvements and addressing boundary condition challenges.

Contribution

It presents a novel gauge-fixed Fourier acceleration approach integrated into hybrid Monte Carlo for lattice gauge simulations, with initial results and strategies for large-volume applications.

Findings

Preliminary autocorrelation time reductions observed.

Use of fixed boundary links to mitigate topological barriers.

Identifies challenges with periodic boundary conditions.

Abstract

For an asymptotically free theory, a promising strategy for eliminating Critical Slowing Down (CSD) is na\"ive Fourier acceleration. This requires the introduction of gauge-fixing into the action, in order to isolate the asymptotically decoupled Fourier modes. In this article, we present our approach and results from a gauge-fixed Fourier-accelerated hybrid Monte Carlo algorithm, using an action that softly fixes the gauge links to Landau gauge. We compare the autocorrelation times with those of the pure hybrid Monte Carlo algorithm. We work on a small-volume lattice at weak coupling. We present preliminary results and obstacles from working with periodic boundary conditions, and then we present results from using fixed, equilibrated boundary links to avoid $\mathbb{Z}_3$ and other topological barriers and to anticipate applying a similar acceleration to many small cells in a large, physically-relevant lattice volume.