Variational study of Mott transition by means of Drude weight and superfluid density

To distinguish a metal from an insulator, the Drude weight (D, zero-frequency component of conductivity) is a useful measure, as Kohn pointed out long ago: D>0(=0) for a metal (insulator). Later, Millis and Coppersmith showed that a variational wave function Ψ _Q in which the key ingredient for a Mott transition (a doublon-holon binding effect) is introduced exhibits D> 0 (metallic) even for sufficiently large correlation strength, namely, a Mott transition is absent from Ψ _Q. In contrast, variational Monte Carlo studies using Ψ _Q confirmed, by studying relevant quantities such as doublon density d and a superconducting correlation function P_d^∞, that Ψ _Q undoubtedly raises a Mott transition. This contradiction has been a long-standing perplexing problem. We definitely settle this problem by adding to Ψ _Q a configuration-dependent phase factor P_θ, which has been hitherto overlooked. This factor appropriately picks out a negative counterpart in D for insulators, so that vanishes. Because P_θ does not affect the quantities such as d and P_d^∞, the previous results of Ψ _Q on the Mott transition remain intact for P_θ Ψ _Q.