Abstract
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.