  We study the Hall response of the Bose-Hubbard model subjected to a magnetic
field. We show that the Hall conductivity is proportional to the particle
density plus an integer. The phase diagram is intersected by topological
transitions between different integer values. These transitions originate from
points in the phase diagram with effective charge conjugation symmetry, and are
attributed to degeneracies in the many body spectrum which serve as sources for
the Berry curvature. We find that extensive regions in the phase diagram
exhibit a negative Hall conductivity, implying that flux flow is reversed in
these regions - vortices there flow upstream. We discuss experimental
implications of our findings.
