Phase diagram of Bose-Fermi mixtures in one-dimensional optical lattices
  The ground state phase diagram of the one-dimensional Bose-Fermi Hubbard model is studied in the canonical ensemble using a quantum Monte Carlo method. We focus on the case where both species have half filling in order to maximize the pairing correlations between the bosons and the fermions. In case of equal hopping we distinguish between phase separation, a Luttinger liquid phase and a phase characterized by strong singlet pairing between the species. True long-range density waves exist with unequal hopping amplitudes. 
Lode Pollet, Matthias Troyer, Kris Van Houcke, Stefan M. A. Rombouts