  We provide an explicit lattice model of bosons with two separately conserved
boson species [$U(1)\times U(1)$ global symmetry] realizing a direct transition
between an integer quantum Hall effect of bosons and a trivial phase, where any
intermediate phase is avoided by an additional symmetry interchanging the two
species. If the latter symmetry is absent, we find intermediate superfluid
phases where one or the other boson species condenses. We know the precise
location of the transition since at this point our model has an exact non-local
anti-unitary particle-hole-like symmetry that resembles particle-hole symmetry
in the lowest Landau level of electrons. We exactly map the direct transition
to our earlier study of the self-dual line of the easy-plane NCCP1 model, in
the mathematically equivalent reformulation in terms of two (new) particles
with $\pi$-statistics and identical energetics. While the transition in our
model is first-order, we hope that our mappings and recent renewed interest in
such self-dual models will stimulate more searches for models with a continuous
transition.
