Topological classification of gapped spin chains: Quantized Berry phase as a local order parameter

2007/10/31 by Takaaki Hirano, Hosho Katsura, Yasuhiro Hatsugai · 3 citations
Physics and Astronomy · #Physics of Superconductivity and Magnetism #Quantum many-body systems #Topological Materials and Phenomena #cond-mat.stat-mech #cond-mat.str-el

paper · pdf · doi:10.1103/physrevb.77.094431

published as Phys. Rev. B 77, 094431 (2008) · 6 pages, 4 figures, accepted for publication in Phys. Rev. B

arxiv created 2008/03/25 · openalex publication_date 2008/03/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We characterize several phases of gapped spin systems by local order parameters defined by quantized Berry phases [Y. Hatsugai, J. Phys. Soc. Jpn. 75, 123601 (2006)]. 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 model. The relation between the present Berry phases and the fractionalization in the integer spin chains are discussed as well.

Citations

• Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
• Exact analysis of entanglement in gapped quantum spin chains
• Quantal phase factors accompanying adiabatic changes
• Continuum dynamics of the 1-D Heisenberg antiferromagnet: Identification with the O(3) nonlinear sigma model

Cited by

• Projectification of point group symmetries with a background flux and Lieb-Schultz-Mattis theorem
• Topological identification of a spin-12two-leg ladder with four-spin ring exchange
• Flux insertion, entanglement, and quantized responses