Phase transitions in Bose-Fermi-Hubbard model in the heavy fermion limit: Hard-core boson approach

Abstract

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.

Bose-Fermi-Hubbard model in the truncated Hilbert space limit

“…Consideration in the hard-core boson limit allows one to describe SF-MI transitions in the regions of the MI lobes contact points. The n b 2 restriction enables one to analyze the more general case of On the left-hand side: hard-core bosons, ground state diagram for n B 1 is taken from [1]; the diagram for n B 2 case (on the right-hand side); T = 0.005U . [1].…”

“…where separate (2×2) blocks correspond to the states with n f i = 0 and n f i = 1 , respectively. Its eigenvalues are equal to (see [1]):…”

“…Minimization of Ω(ϕ) with the help of equation ∂Ω/∂ϕ = 0 determines the stable equilibrium states of the system. At T = 0, the problem can be solved analytically [1]. 2.…”

“…In order to compare different (with different maximal number of bosons on site) approximations we can use the earlier obtained (see [1]) for the case of n B 1 (hard-core bosons) phase diagrams constructed in this work. In figure 4, the diagram (µ, µ ) is presented.…”

“…The regime of fixed values of chemical potentials (µ and µ , respectively) of Bose-and Fermi-particles is the basic one in our study. Analyzing the behavior of the BE condensate order parameter and the grand canonical potential, we have built, for the case of hard-core bosons and "heavy" fermions, the (µ, µ ) and (µ, t 0 ) phase diagrams at T = 0 and at nonzero temperatures [1]. It is shown that: i) in the cases when transition to the SF phase is accompanied by the change of the mean number of fermions, the PT order changes from the 2nd to the 1st one; this result corresponds to the literature data (DMRG calculations for harmonic trap [2]); ii) the shape of the MI phase regions (so-called lobes) in the (µ, t 0 ) diagrams and the localization of the 1st order PT segments upon them depend on the µ level position.…”