Phase diagrams of the Bose-Hubbard model at finite temperature

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 superfluid and Mott insulator phases are established and the (µ, t) (the chemical potentialtransfer parameter) phase diagrams are built. The effect of temperature change on this transition is analyzed and the phase diagram in the (T, µ) 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.

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

“…At the fixed value of the boson chemical potential (and fixed value of the fermion concentration) there are two critical temperatures at which the phase transition from the Mott insulator to the SF phase takes place. A similar effect is also present in the case of the Bose-Hubbard model; as was supposed in [16] the lower critical temperature can be related to the transition to the superionic state in the superionic crystals.…”

“…In comparison with pure Bose-Hubbard model (see e.g. [16]) the critical temperatures of transition into SF phase at the presence of fermions are lower (besides that, new regions with SF phase appear; at U /U =0,5 they are located around half-integer values of the µ/U ratio). We also depicted the (T, µ) diagram for the case of thermal activation of boson hopping.…”

“…We use the random phase approximation (which is an analogy to the Hubbard-I approximation in the case of the fermionic Hubbard model and is a basic one for the usual Bose-Hubbard model, see [15,16]) and perform the following decoupling:…”

“…We also depicted the (T, µ) diagram for the case of thermal activation of boson hopping. Such a possibility was considered in [16], having in mind the application of BH-model to the ionic conductors. We have rewritten the parameter of the bosonic (ionic in the case of ionic conductors) hopping in the form: t = t 0 exp(−β∆) that can be obtained as a result of renormalization due to the interaction with phonons.…”

Bose-Einstein condensation and/or modulation of "displacements" in the two-state Bose-Hubbard model

“…In the limit U → ∞ (corresponding to the case of the so-called hard-core bosons (HCB), i.e., no more than one boson per site, n i 1), this theory is applicable to the region where the two above-mentioned lobes connect at T = 0 [8]. Being rather some kind of approximation, the HCB model is still widely exploited for a description of the Bose-Einstein condensate (BEC) in optical lattices (see [9]).…”