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 Falikov-Kimball models, respectively. We have shown that the insulator state emerges at half filling due to hybridization of fermions of different bands with momenta $\text{k}$ and $\text{k}+\pi$. 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 Falikov-Kimball models within the framework of the same mechanism for an arbitrary dimension of the system.

中文翻译：

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具有现场库仑排斥的双能带费米子模型中的莫特跃迁

我们提供了两带费米子模型的解析解和数值解，其中包含半填充的现场库仑。在生成带和一个平坦带的极限情况下，该模型分别简化为 Hubbard 和 Falikov-Kimball 模型。我们已经证明，由于不同能带的费米子与动量 $\text{k}$ 和 $\text{k}+\pi$ 的杂交，绝缘体状态在半填充时出现。这种杂化破坏了每个带中粒子数量的守恒，莫特跃迁是自发对称性破坏的结果。根据现场库仑排斥的大小和链带的宽度以及方形和立方晶格计算光谱中的间隙。