  We propose an order parameter to characterize valence-bond-solid (VBS) states
in quantum spin chains, given by the ground-state expectation value of a
unitary operator appearing in the Lieb-Schultz-Mattis argument. We show that
the order parameter changes the sign according to the number of valence bonds
(broken valence bonds) at the boundary for periodic (open) systems. This allows
us to determine the phase transition point in between different VBS states. We
demonstrate this theory in the successive dimerization transitions of the
bond-alternating Heisenberg chains, using the quantum Monte Carlo method.
