Frustrated three-leg spin tubes: from spin 1/2 with chirality to spin 3/2

TL;DR

This paper studies a frustrated three-leg spin tube, revealing a phase transition from a gapped dimerized state to a gapless spin-3/2 chain, with implications for a real material.

Contribution

It demonstrates a first-order phase transition in a frustrated spin tube from a spin-chirality model to an effective spin-3/2 model using DMRG and exact diagonalization.

Findings

First-order phase transition between gapped and gapless phases.

Presence of a 1/3 magnetization plateau.

System effectively behaves as a spin-3/2 chain.

Abstract

Motivated by the recent discovery of the spin tube [(CuCl$_2$tachH)$_3$Cl]Cl$_2$, we investigate the properties of a frustrated three-leg spin tube with antiferromagnetic intra-ring and inter-ring couplings. We pay special attention to the evolution of the properties from weak to strong inter-ring coupling and show on the basis of extensive density matrix renormalization group and exact diagonalization calculations that the system undergoes a first-order phase transition between a dimerized gapped phase at weak coupling that can be described by the usual spin-chirality model and a gapless critical phase at strong coupling that can be described by an effective spin-3/2 model. We also show that there is a magnetization plateau at 1/3 in the gapped phase and slightly beyond. The implications for [(CuCl$_2$tachH)$_3$Cl]Cl$_2$ are discussed, with the conclusion that this system behaves essentially as a spin-3/2 chain.