Fermion Spectrum Of Bose-Fermi-Hubbard Model In The Phase With Bose-Einstein Condensate

Abstract

We investigate the fermion spectrum within the Bose-Fermi-Hubbard model used for the description of boson-fermion mixtures of ultra-cold atoms in optical lattices. We used the method based on the Hubbard operator approach for an on-site basis. The equation for fermion Green's function in the Bose-Fermi-Hubbard model is built; Green's functions of higher orders are decoupled in the Hubbard-I approximation (the case of the strong on-site interaction). The corresponding spectral densities are calculated. In the case of hard-core bosons, the condition of appearance of additional bands in the fermion spectrum is investigated. It is shown that these bands exist only in the state with a Bose-Einstein condensate and appear because of the mixing of states with different numbers of bosons. These additional bands can be interpreted as a manifestation of composite excitations (when the appearance of a fermion on the site is accompanied by the simultaneous creation (or annihilation) of a boson).

Third-Order Correlation Functions for a Coulomb Pair

“…It can also describe the effects of particle pairing and correlation. The Bogolyubov transformations [7] and various models such as the Hubbard model [8] and others (see, e.g., [9]) are also widely used. However, the task c ○ V.I.…”

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

“…In [48], the phase diagrams and phase separation or charge modulation conditions at the ion intercalation in semiconductor crystals were investigated based on the BFH-type model; in [49,50], within pseudospin-fermion description (that corresponds to the above mentioned U → ∞ limit) the conditions of the appearance of SS and CDW phases under effective interparticle interactions were investigated. For the four-state model, that arises in this case, the calculations for fermion band spectrum in Hubbard-I approximation were performed, and its transformation during transition to the SF-phase and at the presence of a Bose-Einstein condensate [51] was investigated.…”