Exact bond ordered ground state for the transition between the band and the Mott insulator

We derive an effective Hamiltonian H(eff) for an ionic Hubbard chain, valid for tt) and the Mott insulator (MI) (U-Delta>t). Using spin-particle transformations Phys. Rev. Lett. 86, 1082 (2001)]], we map H(eff)(U=Delta) into an SU(3) antiferromagnetic Heisenberg model whose exact ground state is known. In this way, we show rigorously that a spontaneously dimerized insulating ferroelectric phase appears in the transition region between the BI and the MI.