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

Abstract

We derive an effective Hamiltonian $H_{eff}$ for an ionic Hubbard chain, valid for $t\ll U,Δ$, where $t$ is the hopping, $U$ the Coulomb repulsion, and $Δ$ the charge transfer energy. $H_{eff}$ is the minimal model for describing the transition from the band insulator (BI) ($Δ-U\gg t$) and the Mott insulator (MI) ($U-Δ\gg t$). Using spin-particle transformations (Phys. Rev. Lett. \textbf{86}, 1082 (2001)), we map $H_{eff}(U=Δ)$ 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 MI.