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.

The static and dynamic dielectric susceptibility of the pseudospin-electron model is investigated in the random phase approximation. The possibility of the phase transition to the homogeneous phase, to the phase with doubly modulated lattice period and to the incommensurate phase is revealed in the regime µ = const depending on the value of the chemical potential. The phase separation on the homogeneous and phase with doubly modulated lattice period is established and the phase diagrams (n, h) are built. The influence of the tunnelling-like splitting on the phase transition picture is studied. The presence of pseudospin-wave excitations and the smooth excitation spectrum and the possibility of their superimposing are revealed.

The lattice model which can be employed for the description of intercalation of ions in crystals is considered in this work. Pseudospin formalism is used in describing the interaction of electrons with ions. The possibility of hopping of intercalated ions between different positions is taken into account. The thermodynamics of the model is investigated in the mean field approximation. Phase diagrams are built. It is shown that at high values of the parameter of ion transfer, the phase transition to a modulated phase disappears. : 64.75.+g, 71.20.Tx, Theoretical description of intercalation of ions in crystals appears to be an urgent problem because metal oxides are very promising electrode materials as hosts for ion (e. g., lithium) insertion. In [1-3] quantum chemical Hartree-Fock and density-functional calculations were performed to investigate lithium intercalation in TiO 2 crystals. It was shown that Li is almost fully ionized once intercalated (Li looses its valence electron). It was revealed that reconstruction of electron spectrum at intercalation takes place. Thus, ion-electron interaction can play a significant role. At intercalation of lithium in TiO 2 , phase separation into Li-poor (Li ∼0.01 TiO 2 ) and Li-rich (Li ∼0.5−0.6 TiO 2 ) phases occurs. This two-phase behaviour leads to a constant value of electrochemical potential [4,5]. In [6], the theoretical investigation of intercalation was performed using the Hamiltonian which included the interaction between ions only. In our previous work [7] we formulated the pseudospinelectron model of intercalation and took into account the ion-electron interaction. It was shown that the effective attractive interaction between ions is formed due to the pseudospin-electron interaction and thus the condition of the appearance of phase transition was established. It was found that the capacity of the system increases near the phase transition point. In the present paper we consider the possibility of a transfer of intercalated ions and investigate the thermodynamics of the model. Key words: intercalation, phase transition, pseudospin-electron model PACSThe Hamiltonian of the model is written as follows:The pseudospin variable S z i takes two values; S z i = 1/2 when there is a lithium ion in a site i and S z i = −1/2 when there is no lithium ion, c + iσ and c iσ are electron creation and annihilation operators, respectively. We consider the possibility of ion and electron jumps between sites (the first and the second term in (1)) and interaction of electrons with lithium ions (g term); µ and h play the role of chemical potentials of electrons and Li ions, respectively. The Hamiltonian is similar to the one used in describing a system of coexisting itinerant electrons and local pairs when the creation and destruction operators for local pairs (hard-core bosons) obey the Pauli spin 1/2 commutation rules (for example, see [9]). However, it should be noted that in [9] the chemical potential of the local pairs and itinerant electrons was the same and the regime of a fi...

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.

Anharmonic phonon contributions to Raman scattering in locally anharmonic crystal systems in the framework of the pseudospin-electron model with tunneling splitting of levels are investigated. The case of strong pseudospin-electron coupling is considered. Pseudospin and electron contributions to scattering are taken into account. Frequency dependences of Raman scattering intensity for different values of model parameters and for different polarization of scattering and incident light are investigated.