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We study the superfluid to Mott insulator transition of a mixture of heavybosons and light fermions loaded in an optical lattice. We focus on the effectof the light fermions on the dynamics of the heavy bosons. It is shown that,when the lattice potential is sufficiently deep to confine the bosons to onedimension but allowing the fermions to freely move in three dimensions (i.e. amixed-dimensionality lattice), the fermions act as an ohmic bath for bosonsleading to screening and dissipation effects on the bosons. Using aperturbative renormalization-group analysis, it is shown that thefermion-induced dissipative effects have no appreciable impact on thetransition from the superfluid to the Mott-insulator state at integer filling.On the other hand, dissipative effects are found to be very important in thehalf-filled case near the critical point. In this case, in the presence of afinite incommensurability that destabilizes the Mott phase, the bosons canstill be localized by virtue of dissipative effects.

Dissipative Effects on the Superfluid to Insulator Transition in Mixed-dimensional Optical Lattices