Bloch Waves, Magnetization and Domain Walls: The Case of the Gluon Propagator

TL;DR

This paper applies Bloch's theorem to lattice gauge configurations in SU(Nc) Yang-Mills theory, enabling larger lattice analysis, improved visualization of gauge-fixed states, and more efficient computation of large-volume observables.

Contribution

It introduces a novel approach using Bloch waves for gauge fixing in lattice gauge theory, enhancing visualization and computational efficiency for large lattices.

Findings

Visualization of gauge-fixed configurations as magnetization domains.

Improved understanding of allowed momenta in gauge field evaluation.

Enhanced computational efficiency for large-volume observables.

Abstract

We expand our previous study [1] of replicated gauge configurations in lattice SU(Nc) Yang-Mills theory -- employing Bloch's theorem, from condensed-matter physics -- to construct gauge-fixed field configurations on significantly larger lattices than the original, or primitive, one. We present a comprehensive discussion of the general gauge-fixing problem, identifying advantages of the replicated-lattice approach. In particular, the consideration of Bloch waves leads us to a visualization of the extended gauge-fixed configurations in terms of (color) magnetization domains. Moreover, we are able to explore features of the method to optimize the evaluation of gauge fields in momentum space, furthering our knowledge of the ``allowed momenta'', an issue that has hindered wider applications of this approach up to now. Interestingly, our analysis yields both a better conceptual understanding of the problem and a more efficient way to compute the desired large-volume observables.