Metal-insulator transition in the Hubbard model with a magnetic field: Exact results

The Hubbard model with unit concentration of electrons per one site in the external magnetic field H is considered. In the H→∞ limit the ground state is ferromagnetic and dielectric. A decrease of H results in the phase transition to a new ground state. The electric properties of this state depend on (1) the lattice dimensionality and (2) the U/t ratio (U,t are the standard parameters of the Hubbard model). The linear [one-dimensional (1D)], square (2D), and simple cubic (3D) lattices are considered. In the 1D and 2D cases the new ground state is always dielectric. In the 3D case this state is dielectric only at U/(12t)>${\mathit{W}}^{\mathrm{-}1}$, where W=1.516. . . is the Watson integral. At U/(12t)<${\mathit{W}}^{\mathrm{-}1}$ it becomes a conducting one. The line of phase transition with respect to the field is constructed in the H-U coordinates. It is found that the transition to the dielectric state results in the transformation of the ferromagnetic order to the spin-flip phase. The transition to the conducting state results only in a decrease of the average local spin.