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We study the Bose-Fermi mixture with infinitely boson-boson repulsion andfinite boson-Fermion repulsion. By using a generalized Jordan-Wignertransformation, we show that the system can be mapped to a repulsive Hubbardmodel and thus can be solved exactly for the case with equal boson and fermionmasses. By using the Bethe-ansatz solutions, we investigate the ground stateproperties of the mixture system. Our results indicate that the system withcommensurate filling $n=1$ is a charge insulator but still a superfluid withnon-vanishing superfluid density. We also briefly discuss the case with unequalmasses for bosons and fermions.

Mixture of Tonks-Girardeau gas and Fermi gas in one-dimensional optical lattices