Maximized string order parameters in the valence bond solid states of quantum integer spin chains

TL;DR

This paper introduces optimized string order parameters for quantum integer spin chains, revealing hidden topological symmetries and topological charges associated with local excitations in valence bond solid states.

Contribution

It proposes a new set of maximized string order parameters involving spin-twist angles, uncovering hidden $Z_{S+1} imes Z_{S+1}$ symmetry and topological charges in valence bond solid states.

Findings

Revealed hidden $Z_{S+1} imes Z_{S+1}$ symmetry in spin chains.

Linked local triplet excitations to $Z_{S+1}$ topological charge.

Introduced optimized string order parameters involving spin-twist angles.

Abstract

We propose a set of maximized string order parameters to describe the hidden topological order in the valence bond solid states of quantum integer spin-S chains. These optimized string order parameters involve spin-twist angles corresponding to $Z_{S+1}$ rotations around $z$ or $x$-axes, suggesting a hidden $Z_{S+1}\times Z_{S+1}$ symmetry. Our results also suggest that a local triplet excitation in the valence bond solid states carries a $Z_{S+1}$ topological charge measured by these maximized string order parameters.