Abstract

The Hubbard model is studied at half filling, using two complementary variational wave functions, the Gutzwiller ansatz for the metallic phase at small values of the interaction parameter U and its analog for the insulating phase at large values of U. The metallic phase is characterized by the Drude weight, which exhibits a jump at the critical point Uc. In the insulating phase the system behaves as a collection of dipoles which increase both in number and in size as U gets smaller. The two wave functions are able to describe the two asymptotic regimes (small and large values of U, respectively), but they can no longer be trusted in the region of the Mott transition (U≈Uc). More powerful methods are needed to study, for instance, the divergence of the electric susceptibility for U→Uc