2020/04/30 by Igor N. Karnaukhov
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Condensed matter physics #Coulomb #Electron #Fermion #Hubbard model #Mott transition #Physics #Physics of Superconductivity and Magnetism #Quantum mechanics #Superconductivity #Topological Materials and Phenomena #cond-mat.str-el
paper · pdf · doi:10.1016/j.aop.2020.168308
published as Annals of Physics, Volume 422, November 2020, 168308 · 12 pages, 5 figures
openalex publication_date 2020/09/25 · arxiv created 2020/10/24 · arxiv updated 2020/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We provide analytical and numerical solution of the two band fermion model with on-site Coulomb at half filling. In limiting cases for generate bands and one flat band, the model reduces to the Hubbard and Falicov-Kimball models, respectively. We have shown that the insulator state emerges at half filling due to hybridization of fermions of different bands with momenta k and k+π. Such hybridization breaks the conservation of the number of particles in each band, the Mott transition is a consequence of spontaneous symmetry breaking. A gap in the spectrum is calculated depending on the magnitude of on-site Coulomb repulsion and the width of the band for the chain, as well as for square and cubic lattices. The proposed approach allows us to describe the formation of the gap in the fermion spectra in the Hubbard and Falicov-Kimball models within the framework of the same mechanism for an arbitrary dimension of the system.