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arXiv · 1009.3792

$Z_Q$ Topological Invariants for Polyacetylene, Kagome and Pyrochlore lattices

Y. Hatsugai·I. Maruyama
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Abstract

Adiabatic $Z_Q$ 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 $Z_Q$ equivalence. As for the chiral symmetric case, a topological form of the $Z_2$-invariant is explicitly given as well.

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Y. Hatsugai, I. Maruyama. 2010-09-20. $Z_Q$ Topological Invariants for Polyacetylene, Kagome and Pyrochlore lattices. https://doi.org/10.1209/0295-5075%2F95%2F20003

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