  We derive an effective Hamiltonian $H_{eff}$ for an ionic Hubbard chain,
valid for $t\ll U,\Delta $, where $t$ is the hopping, $U$ the Coulomb
repulsion, and $\Delta$ the charge transfer energy. $H_{eff}$ is the minimal
model for describing the transition from the band insulator (BI) ($\Delta -U\gg
t$) and the Mott insulator (MI) ($U-\Delta \gg t$). Using spin-particle
transformations (Phys. Rev. Lett. \textbf{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 MI.
