Exact Bond Ordered Ground State for the Transition between the Band and the Mott Insulator

We derive an effective Hamiltonian Heff for an ionic Hubbard chain, valid for tU,Δ, where t is the hopping, U is the Coulomb repulsion, and Δ is the charge-transfer energy. Heff is the minimal model for describing the transition between the band insulator (BI) (Δ-Ut) and the Mott insulator (MI) (U-Δt). Using spin-particle transformations [Phys. Rev. Lett. 86, 1082 (2001)], we map Heff(U=Δ) 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.