  Interacting lattice bosons at integer filling can support two distinct
insulating phases, which are separated by a critical point: the Mott insulator
and the Haldane insulator[Phys. Rev. Lett. 97, 260401 (2006)]. The critical
point can be gapped out by breaking lattice inversion symmetry. Here, we show
that encircling this critical point adiabatically pumps one boson across the
system. When multiple chains are coupled, the two insulating phases are no
longer sharply distinct, but the pumping property survives. This leads to
strict constraints on the topology of the phase diagram of systems of quasi-one
dimensional interacting bosons.
