Emergent SU(3) symmetry in a four leg spin tube

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 SU(3)} 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 SU(3) spin chain. We establish that the correlation functions of ferroquadrupolar operators can be used to reveal the emergent symmetry.