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Excitation Spectrum of One-dimensional Extended Ionic Hubbard Model

We use Perturbative Continuous Unitary Transformations (PCUT) to study the one dimensional Extended Ionic Hubbard Model (EIHM) at half-filling in the band insulator region. The extended ionic Hubbard model, in addition to the usual ionic Hubbard model, includes an inter-site nearest-neighbor (n.n.) repulsion, $V$. We consider the ionic potential as unperturbed part of the Hamiltonian, while the hopping and interaction (quartic) terms are treated as perturbation. We calculate total energy and ionicity in the ground state. Above the ground state, (i) we calculate the single particle excitation spectrum by adding an electron or a hole to the system. (ii) the coherence-length and spectrum of electron-hole excitation are obtained. Our calculations reveal that for V=0, there are two triplet bound state modes and three singlet modes, two anti-bound states and one bound state, while for finite values of $V$ there are four excitonic bound states corresponding to two singlet and two triplet modes. The major role of on-site Coulomb repulsion $U$ is to split singlet and triplet collective excitation branches, while $V$ tends to pull the singlet branches below the continuum to make them bound states.