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.
We study the phase diagram of the zero-temperature, one-dimensional Bose-Fermi-Hubbard model for fixed fermion density in the limit of small fermionic hopping. This model can be regarded as an instance of a disordered Bose-Hubbard model with dichotomic values of the stochastic variables. Phase boundaries between compressible, incompressible (Mott-insulating), and partially compressible phases are derived analytically within a generalized strong-coupling expansion and numerically using density matrix renormalization group (DMRG) methods. We show that first-order correlations in the partially compressible phases decay exponentially, indicating a glass-type behavior. Fluctuations within the respective incompressible phases are determined using perturbation theory and are compared to DMRG results.
It is shown that in the Bose-Fermi-Hubbard model which is used for a description of the ultracold atomic boson-fermion mixture in the optical lattice, the
nB⩽2 restriction enables one to analyze a more general case of separated lobes Mott insulator in comparison with the case of
nB⩽1 (hard-core bosons). It also showed that the restriction to no more than 2 bosons on site is enough to comprehend the structure of
(μ,∣t0∣) diagrams at arbitrary
nb values with an account of a possibility of the 1st order phase transition.