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We investigate a model of hard-core bosons with correlated hopping on thehoneycomb lattice in an external magnetic field by means of a coupled-wireapproach. It has been numerically shown that this model exhibits at halffilling the bosonic integer quantum Hall (BIQH) state, which is asymmetry-protected topological phase protected by the $U(1)$ particleconservation [Y.-C. He et al., Phys. Rev. Lett. 115, 116803 (2015)]. Bycombining the bosonization approach and a coupled-wire construction, weanalytically confirm this finding and show that it even holds in the stronglyanisotropic (quasi-one-dimensional) limit. We discuss the stability of the BIQHphase against tunneling that break the separate particle conservations ondifferent sublattices down to a global particle conservation. We further arguethat a phase transition between two different BIQH phases is in a deconfinedquantum critical point described by two copies of the (2+1)-dimensional $O(4)$nonlinear sigma model with the topological $\theta$ term at $\theta=\pi$.Finally we predict a possible fractional quantum Hall state, the Halperin (221)state, at 1/6 filling.

Bridging coupled wires and lattice Hamiltonian for two-component bosonic quantum Hall states