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Dispersive Excitations in the One-Dimensional Ionic Hubbard Model

A detailed study of the one-dimensional ionic Hubbard model with interaction $U$ is presented. We focus on the band insulating (BI) phase and the spontaneously dimerized insulating (SDI) phase which appears on increasing $U$. By a recently introduced continuous unitary transformation [Krull et al.\ Phys. Rev. B {\bf 86}, 125113 (2012)] we are able to describe the system even close to the phase transition from BI to SDI although the bare perturbative series diverges before the transition is reached. First, the dispersion of single fermionic quasiparticles is determined in the full Brillouin zone. Second, we describe the binding phenomena between two fermionic quasiparticles leading to an $S=0$ and to an $S=1$ exciton. The latter corresponds to the lowest spin excitation and defines the spin gap which remains finite through the transition from BI to SDI. The former becomes soft at the transition indicating that the SDI corresponds to a condensate of these $S=0$ excitons. This view is confirmed by a BCS mean field theory for the SDI phase.