Abstract
The phase transitions in the Bose-Hubbard model are investigated. A single-particle Green’s function is calculated in the random phase approximation and the formalism of the Hubbard operators is used. The regions of existence of the superuid and Mott insulator phases are established and the (; t) (the chemical potential n transfer parameter) phase diagrams are built. The effect of temperature change on this transition is analyzed and the phase diagram in the (T; ) plane is 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.
Highlights
The Bose-Hubbard model (BHM) has been intensively investigated in the last 15 years
A special attention will be paid here to the investigation of the effect of thermal activation of the ion hopping on the shape of phase diagrams
We introduce the on-site basis |n i (n is a number of bosons on a site i) and use the Hubbard operators Xinm = |n i m|i
Summary
The Bose-Hubbard model (BHM) has been intensively investigated in the last 15 years. The model of Bose-Hubbard type can be useful for investigation of ionic conductivity in crystalline ionic conductors, but it can be applied to description of the intercalation in crystals [11] and kinetics of ionic adsorption on the crystal surfaces [12]. A special attention will be paid here to the investigation of the effect of thermal activation of the ion hopping on the shape of phase diagrams (we take into account the temperature dependence of the transfer parameter). The effect of thermal activation can be important in the case of ionic conductors It was not studied in the framework of the BHM; such an investigation has been performed only in the hard-core boson limit [14] so far
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