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

Understand

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.