We consider an antiferromagnetic four-leg spin-1/2 tube using Abelian and non-Abelian bosonization. We show that in the limit of weak interchain coupling, the most relevant interaction gives rise to an emergent $\mathrm{SU}\left(3\right)$ symmetry, broken only by marginal interactions that can be canceled by diagonal interchain couplings. We discuss the low-energy spectrum in the semiclassical limit and using a mapping to a trimerized $\mathrm{SU}\left(3\right)$ spin chain. We establish that the correlation functions of ferroquadrupolar operators can be used to reveal the emergent symmetry.

• Received 16 February 2024
• Revised 9 April 2024
• Accepted 6 May 2024

DOI:https://doi.org/10.1103/PhysRevB.109.174430