  We propose to use quantized Berry phases as local order parameters of gapped
quantum liquids, which are invariant under some anti-unitary operation. After
presenting a general prescription, the scheme is applied for Heisenberg models
with frustrations and two dimensional extended Su-Schrieffer-Heeger models
associated with a random dimer covering. In each phases, the quantized Berry
phases, as 0 or $\pi$, describe the ground state texture pattern of local
singlet bonds and dimer bonds. Also possible applications to large classes of
correlated electron systems are discussed.
