# 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

## TL;DR

This paper constructs a lattice model of bosons with two conserved species that exhibits a direct transition between a bosonic integer quantum Hall state and a trivial insulator, connecting it to the self-dual line in the easy-plane NCCP1 model.

## Contribution

The authors explicitly realize a lattice model with a direct transition between quantum Hall and trivial phases, linking it to the self-dual NCCP1 model and exploring the nature of the transition.

## Key findings

- Transition is first-order in the model.
- Exact mapping to the self-dual NCCP1 line.
- Intermediate superfluid phases occur without symmetry.

## Abstract

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.