Scaling and Luescher Term in a non-Abelian (2+1)d SU$(2)$ Quantum Link Model

TL;DR

This paper uses tensor network methods to study a 2+1 dimensional non-Abelian SU(2) quantum link model, revealing confining behavior, a Lüscher term, and a rough string regime across various coupling strengths.

Contribution

It provides the first detailed tensor network analysis of the confining potential and string properties in a non-Abelian quantum link model in 2+1 dimensions.

Findings

The theory is confining across all studied couplings.

A clear Lüscher term with a coupling-dependent coefficient is observed.

String width scales logarithmically with length, indicating a rough string without a roughening transition.

Abstract

We investigate a non-Abelian SU$(2)$ quantum link model in $2+1$ dimensions on a hexagonal lattice using tensor network methods. We determine the static quark potential for a wide range of bare coupling values and find that the theory is confining. We also probe the existence of a L\"uscher term and find a clear signal with a $g^2$ dependent coefficient, in qualitative agreement with a strong coupling expansion. Correspondingly, the width of the strings scales logarithmically with the string length again for all $g^2$-values, providing evidence for a rough string, with no indication for a roughening transition.