The dimerized phase of ionic Hubbard models

TL;DR

This paper derives an effective Hamiltonian for the ionic Hubbard model at half filling, revealing a dimerized phase with properties like ferroelectricity and fractional charge excitations, using spin-particle transformations and bosonization.

Contribution

It introduces a novel effective Hamiltonian for the ionic Hubbard model and maps it onto known spin models, providing insights into the dimerized phase and its properties.

Findings

The effective model exhibits a spontaneously dimerized ground state.

Polarization is proportional to the charge of elementary excitations.

Properties like ferroelectricity and fractional charge are discussed.

Abstract

We derive an effective Hamiltonian for the ionic Hubbard model at half filling, extended to include nearest-neighbor repulsion. Using a spin-particle transformation, the effective model is mapped onto simple spin-1 models in two particular cases. Using another spin-particle transformation, a slightly modified model is mapped into an SU(3) antiferromagnetic Heisenberg model whose exact ground state is known to be spontaneously dimerized. From the effective models several properties of the dimerized phase are discussed, like ferroelectricity and fractional charge excitations. Using bosonization and recent developments in the theory of macroscopic polarization, we show that the polarization is proportional to the charge of the elementary excitations.