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Drude weight ($D$) is a useful measure to distinguish a metal from aninsulator. However, $D$ has not been justifiably estimated by the variationtheory for long, since Millis and Coppersmith [Phys. Rev. B 43 (1991) 13770]pointed out that a variational wave function $\Psi_Q$, which includes the keyingredient (doublon-holon binding effect) for a Mott transition, yields apositive $D$ (namely metallic) even in the Mott-insulating regime. We arguethat, to obtain a correct $D$, an imaginary part must exist in the wavefunction. By introducing a configuration-dependent phase factor ${\calP}_\theta$ to $\Psi_Q$, Mott transitions are successfully represented by $D$($D=0$ for $U>U_{\rm c}$) for a normal and $d$-wave pairing states; thereby,the problem of Millis and Coppersmith is settled. Generally, ${\cal P}_\theta$plays a pivotal role in describing current-carrying states in regimes of Mottphysics. On the other hand, we show using a perturbation theory, the one-body(mean-field) part of the wave function should be complex for band insulatorssuch as antiferromagnetic states in hypercubic lattices.

Drude and Superconducting Weights and Mott Transitions in Variation Theory