  We characterize several phases of gapped spin systems by local order
parameters defined by quantized Berry phases. This characterization is
topologically stable against any small perturbation as long as the energy gap
remains finite. The models we pick up are $S=1,2$ dimerized Heisenberg chains
and S=2 Heisenberg chains with uniaxial single-ion-type anisotropy.
Analytically we also evaluate the topological local order parameters for the
generalized Affleck-Kennedy-Lieb-Tasaki (AKLT) model. The relation between the
present Berry phases and the fractionalization in the integer spin chains are
discussed as well.
