Topological Classification of Gapped Spin Chains :Quantized Berry Phase as a Local Order Parameter

TL;DR

This paper introduces a topological classification of gapped spin chains using quantized Berry phases as local order parameters, providing a stable way to identify different phases in these quantum systems.

Contribution

It demonstrates how quantized Berry phases serve as topologically stable local order parameters for classifying phases in gapped spin chains, including analytical evaluation for AKLT models.

Findings

Berry phases effectively distinguish different gapped phases.

Topological stability of order parameters under small perturbations.

Analytical results for AKLT and related models.

Abstract

We characterize several phases of gapped spin systems by local order parameters defined by quantized Berry phases. This characterization is topologically stable against any small perturbation as long as the energy gap remains finite. The models we pick up are $S=1,2$ dimerized Heisenberg chains and S=2 Heisenberg chains with uniaxial single-ion-type anisotropy. Analytically we also evaluate the topological local order parameters for the generalized Affleck-Kennedy-Lieb-Tasaki (AKLT) model. The relation between the present Berry phases and the fractionalization in the integer spin chains are discussed as well.