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

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

2007-10-23

arxiv.org/abs/0710.4198v2

Phys. Rev. B 77, 094431 (2008)

Physics

Condensed Matter

Strongly Correlated Electrons

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

Scientific paper

10.1103/PhysRevB.77.094431

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.

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