  We study a bosonic model with correlated hopping on a honeycomb lattice, and
show that its ground state is a bosonic integer quantum Hall (BIQH) phase, a
prominent example of a symmetry protected topological (SPT) phase. By using the
infinite density matrix renormalization group method, we establish the
existence of the BIQH phase by providing clear numerical evidence: (i) a
quantized Hall conductance with $|\sigma_{xy}|= 2$ (ii) two counter propagating
gapless edge modes. Our simple model is an example of a novel class of systems
that can stabilize SPT phases protected by a continuous symmetry on lattices
and opens up new possibilities for the experimental realization of these exotic
phases.
