Spin gap of the three-leg S=3/2 Heisenberg tube

TL;DR

This study investigates the ground-state properties of the three-leg S=3/2 Heisenberg tube, revealing a persistent spin gap due to spontaneous dimerization, with implications for experimental observation and understanding of valence-bond-solid states.

Contribution

It provides the first detailed analysis of the spin gap behavior and valence-bond-solid states in the three-leg S=3/2 Heisenberg tube using DMRG and Berry phase calculations.

Findings

Spin-excitation gap opens for all coupling regimes.

The gap increases slowly with rung coupling, remaining small in weak and intermediate regimes.

Three types of valence-bond-solid states exist depending on coupling ratios.

Abstract

The ground-state properties of the three-leg S=3/2 Heisenberg tube are studied using the density-matrix renormalization group method. We find that the spin-excitation gap associated with a spontaneous dimerization opens for the whole coupling regime, as seen in the three-leg S=1/2 Heisenberg tube. However, in contrast to the case of S=1/2 tube, the gap increases very slowly with increasing the rung coupling and its size is only a few % or less of the leg exchange interaction in the weak- and intermediate-coupling regimes. We thus argue that, unless the rung coupling is substantially larger than the leg coupling, the gap may be quite hard to be observed experimentally. We also calcuate the quantized Berry phase to show that there exist three kinds of valence-bond-solid states depending on the ratio of leg and rung couplings.