0372-400Х (Edition in Ukrainian)
2071-0186 (Edition in English)
2071-0194 (in electronic form)
Abbreviated key title: Ukr. J. Phys.
Institute for Condensed Matter Physics, Nat. Acad. of Sci. of Ukraine
(1, Svientsitskii Str., Lviv 79011, Ukraine; e-mail: firstname.lastname@example.org)
Fermion Spectrum Of Bose-Fermi-Hubbard Model In The Phase With Bose-Einstein Condensate
Section: Solid matter
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).
Key words: Bose–Fermi–Hubbard model, optical lattices, Green’s function, Bose–Einstein condensate, energy spectrum.