Repulsion-attraction asymmetry in the Bose-Fermi-Hubbard model

It is shown that in the Bose-Fermi-Hubbard model, used for a description of the atomic boson-fermion mixture in the optical lattice, the fermion-hole symmetry allows one to establish a correspondence between cases of the on-site repulsion and attraction. Based on the phase diagrams, built with the help of a corresponding transformation of model parameters within the framework of the grand canonical ensemble, the conditions of the superfluid phase existence at the boson-fermion attraction are analyzed. The phase diagrams that illustrate the difference of behavior of the BF mixture in the cases of BF repulsion or attraction are obtained. A relation to the available experimental data is discussed.