Insulator, metal, or superconductor: The criteria

The appropriate infinite-wavelength ${\mathit{q}}_{\mathit{i}}$→0 and zero-frequency ω→0 limits of the paramagnetic current-current correlation function provide criteria for determining whether a system is insulating, metallic, or superconducting. Here we discuss these criteria for lattice models and present Monte Carlo data for the two-dimensional positive- and negative-U Hubbard models that imply that the ground state of the half-filled positive-U Hubbard model is an insulator, the doped state is a metal, and the negative-U Hubbard model is a superconductor.