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Topological invariants for phase transition points of one-dimensional Z2 topological systems

Author

Listed:
  • Linhu Li

    (Beijing Computational Science Research Center
    CeFEMA, Instituto Superior Técnico, Universidade de Lisboa)

  • Chao Yang

    (Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences)

  • Shu Chen

    (Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences
    Collaborative Innovation Center of Quantum Matter)

Abstract

We study topological properties of phase transition points of two topologically non-trivial Z 2 classes (D and DIII) in one dimension by assigning a Berry phase defined on closed circles around the gap closing points in the parameter space of momentum and a transition driving parameter. While the topological property of the Z 2 system is generally characterized by a Z 2 topological invariant, we identify that it has a correspondence to the quantized Berry phase protected by the particle-hole symmetry, and then give a proper definition of Berry phase to the phase transition point. By applying our scheme to some specific models of class D and DIII, we demonstrate that the topological phase transition can be well characterized by the Berry phase of the transition point, which reflects the change of Berry phases of topologically different phases across the phase transition point.

Suggested Citation

  • Linhu Li & Chao Yang & Shu Chen, 2016. "Topological invariants for phase transition points of one-dimensional Z2 topological systems," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 89(9), pages 1-6, September.
    • Handle: RePEc:spr:eurphb:v:89:y:2016:i:9:d:10.1140_epjb_e2016-70325-x
    DOI: 10.1140/epjb/e2016-70325-x
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    Solid State and Materials;

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