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Phase diagrams of the Bose-Hubbard model at nite temperature

Ihor V. Stasyuk, T. S. Mysakovych

Published Jul 8, 2009• 1 citation
OpenAlex

Abstract

The phase transitions in the Bose-Hubbard model are investigated. A single-particle Green’s function is calculated in the random phase approximation and the formalism of the Hubbard operators is used. The regions of existence of the superuid and Mott insulator phases are established and the (; t) (the chemical potential n transfer parameter) phase diagrams are built. The effect of temperature change on this transition is analyzed and the phase diagram in the (T; ) plane is 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.

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The phase transitions in the Bose-Hubbard model are investigated. A single-particle Green’s function is calculated in the random phase approximation and the formalism of the Hubbard operators is used. The regions of existence of the superuid and Mott insulator phases are established and the (; t) (the chemical potential n transfer parameter) phase diagrams are built. The effect of temperature change on this transition is analyzed and the phase diagram in the (T; ) plane is 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 phase transitions in the Bose-Hubbard model are investigated. A single-particle Green's function is calculated in the random phase approximation 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)(μ,t)(μ,t) (the chemical potential -- transfer parameter) phase diagrams are built. The influence of temperature change on this transition is analyzed and the phase diagram in the (T,μ)(T,μ)(T,μ) plane is 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 phase transitions in the Bose-Hubbard model are investigated.A single-particle Green's function is calculated in the random phase approximation 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 chemical potentialtransfer parameter) phase diagrams are built.The effect of temperature change on this transition is analyzed and the phase diagram in the (T, µ) plane is 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 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.
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.
The zero temperature phase diagram for ultracold bosons in a random 1D potential is obtained through a site decoupling mean-field scheme performed over a Bose-Hubbard (BH) Hamiltonian, whose hopping term is considered as a random variable. As for the model with random on-site potential, the presence of disorder leads to the appearance of a Bose glass phase. The different phases—i.e., Mott insulator, superfluid, and Bose glass—are characterized in terms of condensate fraction and superfluid fraction. Furthermore, the boundary of the Mott lobes is related to an off-diagonal Anderson model featuring the same disorder distribution as the original BH Hamiltonian.
Building on the work of Fisher et al. [Phys. Rev. B 40, 546 (1989)], we develop the perturbation theory for the Bose-Hubbard model and apply it to calculate the effects of a degenerate gas of spin-polarized fermions interacting by contact interactions with the constituent bosons. For the single-band Bose-Hubbard model, we find that the net effect of the screening of the boson on-site interaction by the fermions is to suppress the Mott-insulating lobes in the Bose-Hubbard phase diagram. For the more general multiband model, we find that, in addition to the fermion screening effects, the virtual excitations of the bosons to the higher Bloch bands, coupled with the contact interactions with the fermions, result in an effective increase (decrease) of the boson on-site repulsion (hopping parameter). If the higher-band renormalization of the boson parameters is dominant over the fermion screening of the interaction, the Mott-insulating lobes in the Bose-Hubbard phase diagram are enhanced for either sign of the Bose-Fermi interactions, consistent with the recent experiments.