https://doi.org/10.1140/epjb/e2016-70325-x
Regular Article
Topological invariants for phase transition points of one-dimensional Z2 topological systems
1 Beijing Computational Science
Research Center, Beijing
100089, P.R.
China
2 CeFEMA, Instituto Superior
Técnico, Universidade de Lisboa, Av. Rovisco
Pais, 1049-001
Lisboa,
Portugal
3 Beijing National Laboratory for
Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences,
Beijing
100190, P.R.
China
4 Collaborative Innovation Center of
Quantum Matter, Beijing, P.R. China
a e-mail: rubilacxelee@gmail.com
Received:
23
May
2016
Received in final form:
4
July
2016
Published online:
12
September
2016
We study topological properties of phase transition points of two topologically non-trivial Z2 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 Z2 system is generally characterized by a Z2 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.
Key words: Solid State and Materials
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2016