  Recently by using quantized Berry phases, a prescription for a local
characterization of gapped topological insulators is given. One requires the
ground state is gapped and is invariant under some anti-unitary operation. A
spin liquid which is realized as a unique ground state of the Heisenberg spin
system with frustrations is a typical target system, since pairwise exchange
couplings are always time-reversal invariants even with frustrations.
  As for a generic Heisenberg model with a finite excitation gap, we locally
modify the Hamiltonian by a continuous SU(2) twist only at a specific link and
define the Berry connection by the derivative. Then the Berry phase evaluated
by the entire many-spin wavefunction is used to define the local topological
order parameter at the link. We numerically apply this scheme for several spin
liquids and show its physical validity.
