Two-state Bose-Hubbard model in the hard-core boson limit

Abstract

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.

Bose-Einstein condensation in the excited band and the energy spectrum of the Bose-Hubbard model

“…This is demonstrated by the behavior of the order parameter ξ given by (9). In the region μ < 0, as shown in [23], the nonzero values of ξ appear smoothly via a second-order transition, while there is an S-like bend on the curve ξ(μ) in the region μ > 0 at sufficiently low temperatures, which indicates a first-order transition. The line of such a transition is determined by the equilibrium condition for the grand canonical potentials Ω = −Θ log Z in the NO and SF phases.…”

“…The spinodals on the plane (Θ, μ) obtained by solving Eq. (10) numerically are given in [23]. The instability with respect to Bose-Einstein condensation appears for δ < |t 0 |.…”

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

“…Beside a study of thermodynamics and the phase transition to the superfluid (SF) phase for such lattices of different structure and dimensionality, collective phenomena caused by interactions of various type are another matter of interest. Theoretical description is based on the Bose-Hubbard model (BHM) proposed in works [1,2] and extended by consideration of direct intersite interactions between particles (resulting in the appearance of modulated and separated phases) [3] as well as by taking into account the excited single-site states [4]. The extension of a single-site basis that also takes place in the case of bosons with nonzero spin (e.g., S = 1, [5,6]) leads to more complex phase diagrams where the phase transition to the superfluid phase can change its order from the second to the first one.…”

“…Within the framework of the HCB model extended by an allowance for the first excited local vibrational state, we studied a phase transition to the superfluid phase for the case of a particle transfer over the excited states [4]. It was established that this phase transition can be of the first or of the second order; the system can also separate into normal (NO) and superfluid (SF) phases.…”

“…We will consider the coexistence and the mutual influence of the BEC and the modulation (or the uniform ordering) of the particle displacements. Our description is based on the two-state HCB model where the particle transfer occurs between the local ground states (unlike the excited-state transfer considered in [4,16]). This approach takes into account the peculiarities of boson transfer in the optical lattice with local double-well potentials [17,18].…”