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Motivated by the recent discovery of the spin tube[(CuCl$_2$tachH)$_3$Cl]Cl$_2$, we investigate the properties of a frustratedthree-leg spin tube with antiferromagnetic intra-ring and inter-ring couplings.We pay special attention to the evolution of the properties from weak to stronginter-ring coupling and show on the basis of extensive density matrixrenormalization group and exact diagonalization calculations that the systemundergoes a first-order phase transition between a dimerized gapped phase atweak coupling that can be described by the usual spin-chirality model and agapless critical phase at strong coupling that can be described by an effectivespin-3/2 model. We also show that there is a magnetization plateau at 1/3 inthe gapped phase and slightly beyond. The implications for[(CuCl$_2$tachH)$_3$Cl]Cl$_2$ are discussed, with the conclusion that thissystem behaves essentially as a spin-3/2 chain.Comment: 8 pages, 9 figures, revised versio

physical review. b, condensed matter and materials physics

Frustrated three-leg spin tubes: From spin<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>1</mml:mn><mml:mo>∕</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math>with chirality to spin<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>3</mml:mn><mml:mo>∕</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math>

Frustrated three-leg spin tubes: From spin1∕2with chirality to spin3∕2