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 ΨQ 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. ΨQ In contrast, variational Monte Carlo studies using ΨQ confirmed, by studying relevant quantities such as doublon density d and a superconducting correlation function, Pd∞ that ΨQ undoubtedly raises a Mott transition. This contradiction has been a long-standing perplexing problem. We definitely settle this problem by adding ΨQ to a configuration-dependent phase factor Pθ, which has been hitherto overlooked. This factor appropriately picks out a negative counterpart in D for insulators, so that D vanishes. Because Pθ does not affect the quantities such as d and Pd∞, the previous results of ΨQ on the Mott transition remain intact for PθΨQ.