Computing the static potential using non-string-like trial states

TL;DR

This paper introduces a new method for calculating the static quark-antiquark potential using eigenvector components of the covariant lattice Laplace operator, offering comparable accuracy but improved efficiency especially for fine spatial resolutions.

Contribution

The paper presents a novel approach that replaces Wilson loops with eigenvector-based trial states for potential computation, reducing runtime for detailed spatial analysis.

Findings

Achieved similar statistical errors to Wilson loop methods

Significantly reduced computation time for off-axis separations

Effective in SU(2) Yang-Mills theory

Abstract

We present a method for computing the static quark-antiquark potential, which is not based on Wilson loops, but where the trial states are formed by eigenvector components of the covariant lattice Laplace operator. We have tested this method in SU(2) Yang-Mills theory and have obtained results with statistical errors of similar magnitude compared to a standard Wilson loop computation. The runtime of the method is, however, significantly smaller, when computing the static potential not only for on-axis, but also for many off-axis quark-antiquark separations, i.e. when a fine spatial resolution is required.