  The deconfined quantum critical point, a prototype Landau-forbidden
transition, could exist in principle in the phase transitions involving
symmetry protected topological phase, however, examples of such kinds of
transition in physical systems are rare beyond one-dimensional systems. Here,
using density-matrix renormalization group calculation, we unveil a bosonic
integer quantum Hall phase in two-dimensional correlated honeycomb lattice, by
full identification of its internal structure from the topological $\mathbf{K}$
matrix. Moreover we demonstrate that imbalanced periodic chemical potentials
can destroy the bosonic integer quantum Hall state and drive it into a
featureless trivial (Mott) insulator, where all physical observables evolve
smoothly across the critical point. At the critical point the entanglement
entropy reveals a characteristic scaling behavior, which is consistent with the
critical field theory as an emergent QED$_3$ with two flavors of Dirac
fermions.
