The Haldane phase (HP) is a paradigmatic example of symmetry protected
topological phase. We explore how the bosonic HP behaves in the presence of
local disorder, employing quantum Monte Carlo simulations of an extended
Bose-Hubbard model subject to uncorrelated, quenched disorders. We find that
the HP is robust against a weak disorder and the non-local string order of HP
exhibits a reentrant behavior. Besides, a direct transition between the HP and
superfluid phase is uncovered. A significant part of the ground-state phase
diagram is established for the model, unveiling the location of HP surrounded
by Bose glass, charge density wave and superfluid phases. We also mention a
possible experimental scheme with optical lattice emulator to realize the
present findings.Comment: 6 pages, 5 figure
