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arXiv:1307.2005 · Condensed Matter Physics

Energy spectrum and phase diagrams of two-sublattice hard-core boson model

Stasyuk, Vorobyov

Published Jan 1, 2013• 9 citations
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Abstract

The energy spectrum, spectral density and phase diagrams have been obtained for two-sublattice hard-core boson model in frames of random phase approximation approach.Reconstruction of boson spectrum at the change of temperature, chemical potential and energy difference between local positions in sublattices is studied.The phase diagrams illustrating the regions of existence of a normal phase which can be close to Mottinsulator (MI) or charge-density (CDW) phases as well as the phase with the Bose-Einstein condensate (SF phase) are built.

DOI
10.5488/cmp.16.23005

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The energy spectrum, spectral density and phase diagrams have been obtained for two-sublattice hard-core boson model in frames of random phase approximation approach.Reconstruction of boson spectrum at the change of temperature, chemical potential and energy difference between local positions in sublattices is studied.The phase diagrams illustrating the regions of existence of a normal phase which can be close to Mottinsulator (MI) or charge-density (CDW) phases as well as the phase with the Bose-Einstein condensate (SF phase) are built.
Phase transitions are investigated in the Bose-Fermi-Hubbard model in the mean field and hard-core boson approximations for the case of infinitely small fermion transfer and repulsive on-site boson-fermion interaction.The behavior of the Bose-Einstein condensate order parameter and grand canonical potential is analyzed as functions of the chemical potential of bosons at zero temperature.The possibility of change of order of the phase transition to the superfluid phase in the regime of fixed values of the chemical potentials of Bose-and Fermi-particles is established.The relevant phase diagrams are built.
Phase transition into the phase with Bose-Einstein (BE) condensate in the two-band Bose-Hubbard model with the particle hopping in the excited band only is investigated.Instability connected with such a transition (which appears at excitation energies δ < |t ′ 0 |, where |t ′ 0 | is the particle hopping parameter) is considered.The re-entrant behaviour of spinodales is revealed in the hard-core boson limit in the region of positive values of chemical potential.It is found that the order of the phase transition undergoes a change in this case and becomes the first one; the re-entrant transition into the normal phase does not take place in reality.First order phase transitions also exist at negative values of δ (under the condition δ > δ crit ≈ -0.12|t ′ 0 |).At µ < 0 the phase transition mostly remains to be of the second order.The behaviour of the BE-condensate order parameter is analyzed, the (Θ, µ) and (|t ′ 0 |, µ) phase diagrams are built and localizations of tricritical points are established.The conditions are found at which the separation on the normal phase and the phase with the BE condensate takes place.
The energy spectrum of a system of Bose atoms in the superfluid phase in an optical lattice of the graphene type has been studied. The dispersion laws for the energy bands and the single particle spectral densities are calculated in the random phase approximation and in the framework of the hard-core boson formalism, and their changes at the transition from the normal phase to the superfluid one are described. As a result of this transformation, the number of subbands doubles. In the case of the subband energetic equivalence, the Dirac points in the spectrum survive, and their number becomes twice as much. When the subbands are energetically nonequivalent, the Dirac points are absent. The shape of spectral densities is shown to be sensitive to the changes in the temperature and the chemical potential position.
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.
The spectrum of phonon-like collective excitations in the system of Bose-atoms in optical lattice (more generally, in the system of quantum particles described by the Bose-Hubbard model) is investigated.Such excitations appear due to displacements of particles with respect to their local equilibrium positions.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.Calculations are performed within the random phase approximation in the hard-core boson limit.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.The positions, spectral weights and widths of bands strongly depend on chemical potential of bosons and temperature.The conditions of stability of a system with respect to the lowering of symmetry and displacement modulation are discussed.