  We analyze the disorder driven localization of the two dimensional
Bose-Hubbard model by evaluating the full low energy quasiparticle spectrum via
a recently developed fluctuation operator expansion method. For any strength of
the local interaction we find a mobility edge that displays an approximately
exponential decay with increasing disorder strength. We determine the
finite-size scaling collapse and exponents at this critical line finding that
the localization of excitations is characterized by weak multi-fractality and a
thermal-like critical gap ratio. A direct comparison to a recent experiment
yields an excellent match of the predicted finite-size transition point and
scaling of single particle correlations.
