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 t<<U,Delta, where t is the hopping, U is the Coulomb repulsion, and Delta is the charge-transfer energy. H-eff is the minimal model for describing the transition between the band insulator (BI) (Delta-U>>t) 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.