Krasnov V. Thermodynamics and energy spectra of lattice Bose-Fermi mixtures with strong correlations

Dissertation is devoted to development of the model description of the interacting lattice Bose-Fermi systems for the purpose of study the fermion subsytem influence on their thermodynamical properties and also the features of fermion energy spectrum in the various phase states. Based on the pseudospin-electron model (PEM), the electron spectrum of locally-anharmonic crystals with tunneling splitting of vibrational levels is investigated. The Mott-type transition and reconstruction of spectrum (accompanied by appearance of additional subbands) is analyzed using the alloy analogy approximation within the dynamical mean-field approach. The critical values of the model parameters (such as tunneling frequency, pseudospin-electron interaction constant, local asymmetry field) determining the conditions of emergence and number of electron subbands are found. By application of PEM to describe the ion intercalation in crystals with different filling of electron bands, it was shown that under influence of the electron subsystem and the intersite jumping of impurities the uniform or modulated intercalant distribution, the phase separation, as well as the phases with high mobility of ions can appear. For lattice Bose-Fermi mixture of ultracold atoms in optical lattice which is described by the Bose-Fermi-Hubbard (BFH) model the existence of two types of Bose-Einstein condensate connected with the different filling of fermion states is confirmed; it manifests in appearance of separate regions of SF phase on the phase diagrams at (T = 0). It was also shown, that in the limit of hard-core bosons and “heavy” fermions in such a system, the phase transitions to superfluid phase (SF) in the regime of fixed chemical potentials of particles become of the first order at certain conditions; this leads to phase separation in the case of their fixed concentrations. The area of the SF phase existence, in such a case, changes its topology depending on the magnitude of the boson-fermion interaction and also the temperature and can be simply- or doubly-connected. It was shown that in such a system, in the case of non-zero temperatures, the so-called “re-entrant” transitions ( when the phase with BE condensate is intermediate one) can exist. The fermion spectrum of the BFH model in optical lattice is investigated in the limit of hard-core bosons and strong Hubbard correlation by calculation of one-particle density of states for fermions. It is shown that, if the system is in the state with the Bose-Einstein condensate, the splitting in the fermion spectrum takes place; the additional subbands appear here (due to the new fermion transitions between states with different number of bosons).