Gapped state in three-leg $S=1/2$ Heisenberg tube

TL;DR

This paper investigates the ground state of a three-leg S=1/2 Heisenberg tube, revealing a gapped, dimerized phase with various valence-bond configurations, using advanced numerical methods.

Contribution

It provides the first detailed analysis of the topological and valence-bond structures in the gapped phase of this model, including the effects of ferromagnetic interactions.

Findings

Gapped dimerized state exists even with ferromagnetic leg interactions.

Identified three types of valence-bond configurations depending on exchange ratios.

Topological properties characterized by Berry phase and correlation functions.

Abstract

We study the ground state of three-leg $S=1/2$ Heisenberg tube using the density-matrix renormalization group method. The dimerization order-parameter and spin-excitation gap are calculated in a wide range of leg exchange interactions. We confirm that a gapped state with the dimerization order is realized even when the leg exchange interactions are ferromagnetic. Furthermore, the topological configuration of spin-singlet pairs in the ordered state is determined from the results of the Berry phase of each spin coupling as well as the structure factor of singlet-singlet correlation functions. We find that there exist three kinds of configurations of the valence-bond states depending on the ratio of leg and rung exchange interactions.