ZQ topological invariants for Polyacetylene, Kagome and Pyrochlore lattices
Institute of Physics, University of Tsukuba - 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8571, Japan
2 Graduate School of Engineering Science, Osaka University - Toyonaka, Osaka 560-8531, Japan
Accepted: 1 June 2011
Adiabatic ZQ invariants by quantized Berry phases are defined for gapped electronic systems in d-dimensions (Q=d+1). This series includes Polyacetylene, Kagome and Pyrochlore lattice, respectively for d=1, 2 and 3. The invariants are quantum Q-multimer order parameters to characterize the topological phase transitions by the multimerization. This fractional quantization is protected by the global ZQ equivalence even with particle-particle interaction. As for the chiral symmetric case, a topological form of the Z2 invariant is explicitly given as well.
PACS: 03.65.Vf – Phases: geometric; dynamic or topological / 05.30.Rt – Quantum phase transitions
© EPLA, 2011