Quantum phase transition in the three-leg spin nanotube

Abstract An S = 1 2 three-leg antiferromagnetic spin nanotube is investigated using the DMRG method and the level spectroscopy analysis combined with the numerical exact diagonalization. It is known that the system has a spin gap, when the three rung couplings are equivalent. In this paper, we see that as one of the three rung exchanges varies, a quantum phase transition occurs at a critical value of the varied rung exchange, and then the system is in a gapless Tomonaga–Luttinger-liquid phase. A ground-state phase diagram containing this phase transition is obtained by the phenomenological renormalization.