VARIATIONAL WAVE-FUNCTIONS FOR THE MOTT-HUBBARD TRANSITION

The Hubbard model is investigated at half-filling as a function of the interaction strength U, using two different variational wave function s. The first, due to Gutzwiller, describes a metallic phase, the secon d an antiferromagnetic insulator. The comparison of the variational en ergies yields a transition between a metallic phase for small U to an insulating phase at large U. Three different cases are discussed in so me detail, the one-dimensional chain with long-range hopping (the 1/r Hubbard model), and both the hypercubic and hyperdiamond lattices in t he limit of infinite dimensions.