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We study the quantum phase transition between a band ("ionic") insulator and a Mott-Hubbard insulator, realized at a critical value U = Uc in a bipartite Hubbard model with two inequivalent sites, whose on-site energies differ by an offset Delta. The study is carried out both in D = 1 and D = 2 (square and honeycomb lattices), using exact Lanczos diagonalization, finite-size scaling, and Berry's phase calculations of the polarization. The Born effective charge jump from positive infinity to negative infinity previously discovered in D = 1 by Resta and Sorella is confirmed to be directly connected with the transition from the band insulator to the Mott insulating state, in agreement with recent work of Ortiz et al. In addition, symmetry is analysed, and the transition is found to be associated with a reversal of inversion symmetry in the ground state, of magnetic origin. We also study the D = 1 excitation spectrum by Lanczos diagonalization and finite-size scaling. Not only the spin gap closes at the transition, consistent with the magnetic nature of the Mott state, but also the charge gap closes, so that the intermediate state between the two insulators appears to be metallic. This finding, rationalized within Hartree-Fock as due to a sign change of the effective on-site energy offset Delta for the minority spin electrons, underlines the profound difference between the two insulators. The band-to-Mott insulator transition is also studied and found in the same model in D = 2. There too we find an associated, although weaker, polarization anomaly, with some differences between square and honeycomb lattices. The honeycomb lattice, which does not possess an inversion symmetry, is used to demonstrate the possibility of an inverted piezoelectric effect in this kind of ionic Mott insulator

Born effective charge reversal and metallic threshold state at a band insulator-Mott insulator transition