  The ground-state phase diagram of mixtures of spin polarized fermions and
bosons in a 1D periodic lattice is discussed in the limit of large fermion
hopping and half filling of the fermions. Numerical simulations performed with
the density matrix renormalization group (DMRG) show besides bosonic Mott
insulating (MI), superfluid (SF), and charge density-wave phases (CDW) a novel
phase with spatial separation of MI and CDW regions. We derive an effective
bosonic theory which allows for a complete understanding and quantitative
prediction of the bosonic phase diagram. In particular the origin of CDW phase
and the MI-CDW phase separation is revealed as the interplay between
fermion-induced mean-field potential and long range interaction with
alternating sign.
