  We investigate a model of hard-core bosons with correlated hopping on the
honeycomb lattice in an external magnetic field by means of a coupled-wire
approach. It has been numerically shown that this model exhibits at half
filling the bosonic integer quantum Hall (BIQH) state, which is a
symmetry-protected topological phase protected by the $U(1)$ particle
conservation [Y.-C. He et al., Phys. Rev. Lett. 115, 116803 (2015)]. By
combining the bosonization approach and a coupled-wire construction, we
analytically confirm this finding and show that it even holds in the strongly
anisotropic (quasi-one-dimensional) limit. We discuss the stability of the BIQH
phase against tunneling that break the separate particle conservations on
different sublattices down to a global particle conservation. We further argue
that a phase transition between two different BIQH phases is in a deconfined
quantum 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.
