Fermion Spectrum of Bose–Fermi–Hubbard Model in the Phase with Bose–Einstein Condensate


  • V. O. Krasnov Institute for Condensed Matter Physics, Nat. Acad. of Sci. of Ukraine




Bose–Fermi–Hubbard model, optical lattices, Green’s function, Bose–Einstein condensate, energy spectrum


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).




How to Cite

Krasnov, V. O. (2019). Fermion Spectrum of Bose–Fermi–Hubbard Model in the Phase with Bose–Einstein Condensate. Ukrainian Journal of Physics, 60(5), 443. https://doi.org/10.15407/ujpe60.05.0443



Solid matter