Phase diagrams of the Bose-Fermi-Hubbard model: Hubbard operator approach

Abstract

The phase transitions in the Bose-Fermi-Hubbard model are investigated. The boson Green's function is calculated in the random phase approximation (RPA) and the formalism of the Hubbard operators is used. The regions of existence of the superfluid and Mott insulator phases are established and the (μ,t) (the boson chemical potential vs. hopping parameter) phase diagrams are built at different values of boson-fermion interaction constant (in the regimes of fixed chemical potential or fixed concentration of fermions). The effect of temperature change on this transition is analyzed and the phase diagrams in the (T,μ) plane are constructed. The role of thermal activation of the ion hopping is investigated by taking into account the temperature dependence of the transfer parameter. The reconstruction of the Mott-insulator lobes due to this effect is analyzed.