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Phase transitions in Bose-Fermi-Hubbard model in the heavy fermion limit: Hard-core boson approach

Phase transitions are investigated in the Bose-Fermi-Hubbard model in the mean field and hard-core boson approximations for the case of infinitely small fermion transfer and repulsive on-site boson-fermion interaction. The behavior of the Bose-Einstein condensate order parameter and grand canonical potential is analyzed as functions of the chemical potential of bosons at zero temperature. The possibility of change of order of the phase transition to the superfluid phase in the regime of fixed values of the chemical potentials of Bose- and Fermi-particles is established. The relevant phase diagrams are built.