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

Understand

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.