Localization lengths over metal to band insulator transitions

Density functional and quantum Monte Carlo methods are used to examine the behaviour of the many-electron localization length near band insulator-to-metal transitions in various one- and two-dimensional model systems. The many-electron localization length is infinite in metals and finite in insulators, and is normally assumed to diverge as an insulator-to-metal transition is approached from the insulating side. Our results show that this is not the case: the band insulator-to-metal transition is normally first order and not associated with a diverging length scale. We also identify examples where the localization length diverges but the system is insulating on both sides of the divergence. The usefulness of the localization length as an indicator of the approach of an insulator-to-metal transition is therefore limited. A comparison of our quantum Monte Carlo and density functional results allows us to draw some general conclusions about the effect of correlation on localization.