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 $\delta<\lvert t_0' \rvert$, where $\lvert t_0' \rvert$ 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 $\delta$ (under the condition $\delta>\delta_{\mathrm{crit}}\approx-0.12\lvert t_0' \rvert$). At $\mu<0$ the phase transition mostly remains to be of the second order. The behaviour of the BE-condensate order parameter is analyzed, the $(\Theta,\mu)$ and $(\lvert t_0' \rvert,\mu)$ 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.
Highlights
During the recent years Bose-Hubbard model (BHM) is proved to be a valuable tool in the theory of systems of strongly correlated particles
Phase diagrams in the (|t′0|, n) coordinates are given in figure 9 where the regions of NO, SF and separated phases are shown at various temperatures
As was shown in this work, the transition to the SF phase in the Bose-Hubbard model with two local states on the lattice site can be of the first order in the case, when the particle hopping takes place only in the excited band
Summary
During the recent years Bose-Hubbard model (BHM) is proved to be a valuable tool in the theory of systems of strongly correlated particles. The calculated therein phase diagrams demonstrate that in the simplest case (i.e., hopping of Bose particles in the presence of a single-site Hubbard repulsion) the MI-SF transition is of the second order. An orbital degeneration of the excited p-state is accompanied by anisotropy of hopping parameters and causes the appearance of variously polarized bands in the one-particle spectrum Such bands correspond by convention to different sorts (so-called “flavours”) of bosons and their number correlates with the lattice dimensionality. The issue of BE condensation involving the excited states in the framework of ordinary Bose-Hubbard model was not considered in practice. In the present work we consider an equilibrium thermodynamics of the Bose-Hubbard model taking into account only one nondegenerated excited state on the lattice site besides the ground one. It is convenient to use the formalism of Hubbard operators [31] (standard basis operators [32])
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