  The ferroelectric polarization of perovskite oxides is much larger than
implied by displacement of static ionic charges. We use an explicitly
correlated scheme to investigate the phenomenon; charge transport is evaluated
as a geometric quantum phase. Both covalence and electron-electron interaction
enhance polarization in the weakly correlated regime. At higher values of the
electron-electron interaction, the system undergoes a transition from a band
insulator to a Mott insulator: the static ionic charge is continuous across the
transition, whereas the polarization is discontinuous. Above the transition,
oxygen transports a positive charge.
