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

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.

6 pages, 4 figures, accepted for publication in Phys. Rev. B

References in corpus (2)

• Exact Analysis of Entanglement in Gapped Quantum Spin Chains
• Entanglement Entropy of One-dimensional Gapped Spin Chains

Cited by in corpus (4)

• Degeneracy and Consistency Condition of Berry phases: Gap Closing under the Twist
• Edge states of Spin-1/2 Two-Leg Ladder with Four-Spin Ring Exchange
• Pairwise Entanglement and Geometric Phase in $d=2,3$-Dimensional Free-Fermion Lattice Systems
• The Berry phase: a topological test for the spectrum structure of frustrated quantum spin systems