  In two dimensions strongly interacting bosons in a magnetic field can form an
integer quantum Hall state. This state has a bulk gap, no fractional charges or
topological order in the bulk but nevertheless has quantized Hall transport and
symmetry protected edge excitations. Here we study a simple microscopic model
for such a state in a system of two component bosons in a strong orbital
magnetic field. We show through exact diagonalization calculations that the
model supports the boson integer quantum Hall ground state in a range of
parameters.
