  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.
