Three-dimensional repulsive Hubbard model

Abstract

The three-dimensional repulsive Hubbard model is investigated using the strong-coupling diagram technique. For half-filling, the boundary between paramagnetic and antiferromagnetic states is determined for the range of the Hubbard repulsion $4t\leq U\leq12t$, where $t$ is the hopping integral between neighboring sites. Along this boundary, the density of states is calculated, and it demonstrates the Mott transition at $U\approx9t$. For $U\geq6t$ and half-filling, the density of states has the shape inherent in the strong electron repulsion, while for $U=4t$, its shape points to weak coupling. The dependence of the Néel temperature $T_{\rm N}$ on the electron concentration $\bar{n}$ is investigated for the cases $U=4t$ and $12t$. In the former case, $T_{\rm N}$ decreases monotonously with $\bar{n}$, while in the latter case, there is a plateau in the dependence near $\bar{n}=0.87$. The plateau is connected to a reconstruction of the density of states caused by an effective weakening of electron coupling due to electron depopulation. For $U=12t$ and half-filling, the magnetic critical exponent $γ\approx1.4$, which is close to the value in the Heisenberg model. Some features resembling the first-order phase transition, revealing themselves in a finite crystal, are discussed.