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

physical review. b./physical review. b

Lattice realization of a bosonic integer quantum Hall state - trivial  insulator transition and relation to the self-dual line in the easy-plane  NCCP1 model