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We give a detailed discussion of the recently developed Generalized DynamicalMean-Field Theory (GDMFT) for a mixture of bosonic and fermionic particles. Weshow that this method is non-perturbative and exact in infinite dimensions andreliably describes the full range from weak to strong coupling. Like inconventional Dynamical Mean-Field Theory, the small parameter is 1/z, where zis the lattice coordination number. We apply the GDMFT scheme to a mixture ofspinless fermions and bosons in an optical lattice. We investigate theossibility of a supersolid phase, focussing on the case of 1/2 filling for thefermions and 3/2 filling for the bosons.

Generalized Dynamical Mean-Field Theory for Bose-Fermi Mixtures in Optical Lattices