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

TL;DR

This paper derives an effective Hamiltonian for an ionic Hubbard chain to rigorously demonstrate the emergence of a spontaneously dimerized ferroelectric phase during the transition between band and Mott insulators.

Contribution

It introduces an exact mapping of the transition region Hamiltonian to an SU(3) antiferromagnetic model, revealing the ground state and phase transition details.

Findings

Identification of a spontaneously dimerized ferroelectric phase

Exact ground state derived for the transition region

Rigorous proof of phase transition between BI and MI

Abstract

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.