Velychko O. Quantum lattice models applied to systems with adsorbed or intercalated particles and optical lattices

In the microscopic model approach a range of theoretical descriptions were developed considering the effect of such external factors as pressure, electric field, intercalation (change of chemical potential), etc., on various order-disorder lattice objects. Intercalation of gallium and indium selenide crystals by nickel initiates their electret polarization. A microscopic model of order-disorder type has been proposed that considers redistribution of intercalant atoms between non-polar octahedral and polar tetrahedral positions in the crystal van der Waals gaps. The calculated temperature dependences of dielectric susceptibility qualitatively reproduce experimental results for permittivity. Lithium intercalated anatase used in Li-ion batteries has some special features: coexistence of Li-rich and Li-poor phases as well as two possible positions for Li ions in the oxygen tetrahedron. As shown by the performed symmetry analysis, the intercalation induced lattice deformation can be accompanied by the ordering of antiferroelectric type. A microscopic model for description of the compound is also proposed which combines features of the Mitsui and Blume-Emery-Griffits models and utilizes the symmetry analysis results. A phase separation into the empty and half-filled phases in a wide temperature range has been found closely resembling the phase coexistence in the intercalated crystal. Influence of intercalation on the electronic band structure of the layered nanohybrid compound of the GaSe-type with a stage ordering is studied in the modified version of the periodic Anderson model. Intercalated particles form an additional band like the narrow impurity band or the more extended band hybridized with the main one. The most pronounced transformation of the main band takes place in the vicinity of the impurity level. Phase transition into the phase with the Bose-Einstein condensate in the Bose-Hubbard model with two local states and the particle hopping in the excited band only is investigated. A possibility of separation on the normal phase and the phase with the BE condensate at the fixed average concentration of bosons is demonstrated. For consideration of the non-ergodicity, the single-particle spectral density is calculated in the random phase approximation by means of the temperature boson Green functions. The non-ergodic contribution to the momentum distribution function of particles increases significantly and becomes comparable with the ergodic one in the superfluid phase near the tricritical point. The band spectrum of Bose-atoms in two-dimensional hexagonal optical lattices with the graphene type structure is investigated. The temperature-dependent gapless spectrum with Dirac points placed on the border of Brillouin zone is obtained for the lattice with energetically equivalent sites. Energy spectrum of superfluid phase of the Bose-atom system in the optical lattices of the graphene type is investigated. The spectrum of phonon-like collective excitations in the system of Bose-atoms in optical lattice is investigated. The two-level model taking into account the transitions of bosons between the ground state and the first excited state in potential wells, as well as interaction between them, is used. It is shown that excitation spectrum in normal phase consists of the one exciton-like band, while in the phase with BE condensate an additional band appears. A possibility of modulation, which doubles the lattice constant, as well as the uniform displacement of particles from equilibrium positions are studied. The effects, taking place under external pressure in the SnPS crystal, are investigated in the framework of the deformable Blume-Emery-Griffiths model corresponding to the local potential with three minima. The presence of anomalies in the regions of ferroelectric phase transitions of the first and second order as well as the tricritical point is established; the behaviour of the volume compressibility in these cases is investigated. A simple four-sublattice order-disorder model is proposed for description of dielectric properties of the Rochelle salt crystal. Symmetry properties of the lattice and spatial orientations of effective dipoles are taken into account. An effect of the transverse electric field on spontaneous polarization, shifts of the phase transition points and dielectric susceptibility anomalies is studied.