Variational wave functions and the Mott transition

We prove that a large class of generalized Gutzwiller wave functions, previously believed to be useful in the study of the Mott metal-insulator transition, are always metallic in the sense that the response to an electric field includes a {δ} function at zero frequency (corresponding to free acceleration of carriers in a dc field). We also show that modifying these wave functions to enforce binding of empty and doubly occupied sites is insufficient to produce insulating behavior. We derive a criterion which an insulating wave function must satisfy.