  The effect of bond randomness on the spin-gapped ground state of the spin-1
bond-alternating antiferromagnetic Heisenberg chain is discussed. By using the
loop cluster quantum Monte Carlo method, we investigate the stability of
topological order in terms of the recently proposed twist order parameter [M.
Nakamura and S. Todo: Phys. Rev. Lett. 89 (2002) 077204]. It is observed that
the dimer phases as well as the Haldane phase of the spin-1 Heisenberg chain
are robust against a weak randomness, though the valence-bond-solid-like
topological order in the latter phase is destroyed by introducing a disorder
stronger than the critical value.
