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

We study the quantum phase transition between a band ("ionic") insulator an d a Mott-Hubbard insulator, realized at a critical value U = Uc in a bipart ite Hubbard model with two inequivalent sites, whose on-site energies diffe r by an offset Delta. The study is carried out both in D = 1 and D = 2 (squ are and honeycomb lattices), using exact Lanczos diagonalization, finite-si ze scaling, and Berry's phase calculations of the polarization. The Born ef fective charge jump from positive infinity to negative infinity previously discovered in D = 1 by Resta and Sorella is confirmed to be directly connec ted with the transition from the band insulator to the Mott insulating stat e, in agreement with recent work of Ortiz et al. In addition, symmetry is a nalysed, and the transition is found to be associated with a reversal of in version symmetry in the ground state, of magnetic origin. We also study the D = 1 excitation spectrum by Lanczos diagonalization and finite-size scali ng. Not only the spin gap closes at the transition, consistent with the mag netic 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 e ffective on-site energy offset Delta for the minority spin electrons, under lines 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, wit h some differences between square and honeycomb lattices. The honeycomb lat tice, which does not possess an inversion symmetry, is used to demonstrate the possibility of an inverted piezoelectric effect in this kind of ionic M ott insulator.