MOTT-HUBBARD TRANSITION IN A MAGNETIC-FIELD

We study the density of states (DOS) as a function of the interaction U in the half-filled simplified Hubbard model in a magnetic field. Thi s model is considered on the Bethe lattice in the limit of high dimens ions. We show that the DOS can be calculated exactly, and that many of its properties have an astonishingly simple form. In particular, the DOS can be investigated explicitly in the limits of weak and strong co upling and near the metal-insulator transition. E.g., we find an expli cit result for the critical value U-c, at which the metal-insulator tr ansition occurs, as a function of the magnetization. The relation betw een the magnetization and the magnetic field is calculated numerically . An important result is that the metal-insulator transition, occurrin g in the model with B = 0, is continuously connected to the metal-insu lator transition in the subspace of single spin flips.