Ground state properties of the S = 3/2 three-leg heisenberg tube

Abstract

Using the density-matrix renormalization group and exact diagonalization methods the ground-state properties of the S = 3/2 three-leg Heisenberg tube with leg (J∥) and rung (J⊥) exchange couplings are studied. We find that the spin-excitation gap associated with a spontaneous dimerization opens in the entire region of the coupling strength, as seen in the S = 1/2 three-leg tube. However, in contrast to the case of the S = 1/2 tube, the gap develops very slowly with increasing the rung coupling strength in the weak-coupling regime and its size remains only about 5 % of the leg coupling strength even at J⊥/J∥ = 5. We also calculate the quantized Berry phase and suggest that there exist three types of the valence-bond-solid states depending on the ratio of leg and rung coupling strengths. Moreover, an effective model is derived by the perturbative expansion to check the numerical results in the strong rung-coupling limit.