  The experimentally observed loss of superfluidity by introducing fermions to
the boson Hubbard system on an optical lattice is explained. We show that the
virtual transitions of the bosons to the higher Bloch bands, coupled with the
contact boson-fermion interactions of either sign, result in an effective
increase of the boson on-site repulsion. If this renormalization of the on-site
potential is dominant over the fermion screening of the boson interactions, the
Mott insulating lobes of the Bose-Hubbard phase diagram will be enhanced for
either sign of the boson-fermion interactions. We discuss implications for cold
atom experiments where the expansion of the Mott lobes by fermions has been
conclusively established.

Strongly Correlated Electrons;Quantum Physics