Taking the site-diagonal terms of the ionic Hubbard model (IHM) in one and two spatial dimensions, as H 0 , we employ Continuous Unitary Transformations (CUT) to obtain a "classical" effective Hamiltonian in which hopping term has been renormalized to zero. For this Hamiltonian spin gap and charge gap are calculated at half-filling and subject to periodic boundary conditions. Our calculations indicate two transition points. In fixed , as U increases from zero, there is a region in which both spin gap and charge gap are positive and identical; characteristic of band insulators. Upon further increasing U , first transition occurs at U = U c 1 , where spin and charge gaps both vanish and remain zero up to U = U c 2 . A gap-less state in charge and spin sectors characterizes a metal. For U > U c 2 spin gap remains zero and charge gap becomes positive. This third region corresponds to a Mott insulator in which charge excitations are gaped, while spin excitations remain gap-less.

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.

In our earlier work ͓M. Hafez et al., Phys. Lett. A 373, 4479 ͑2009͔͒ we employed the flow equation method to obtain a classical effective model from a quantum mechanical parent Hamiltonian called, the ionic Hubbard model. The classical ionic Hubbard model ͑CIHM͒ obtained in this way contains solely Fermionic occupation numbers of two species corresponding to particles with ↑ and ↓ spin, respectively. In this paper, we employ the transfer matrix method to analytically solve the CIHM at finite temperature in one dimension. In the limit of zero temperature, we find two insulating phases at large and small Coulomb interaction strength, U, mediated with a gapless phase, resulting in two continuous metal-insulator transitions. Our results are further supported with Monte Carlo simulations.

We investigate single-particle spectral densities and dynamical charge and spin structure factors of the one-dimensional extended ionic Hubbard model in the band insulator regime by using the perturbative continuous unitary transformations method. The one-body staggered potential is considered as the unperturbed part and the hopping term, on-site electron-electron interaction, and the nearest-neighbor repulsive interaction are treated as the perturbations. The excitation spectrum of this model was determined in a previous work (Hafez and Jafari 2010 Eur. Phys. J. B 78 323). It was shown that when the intersite interaction is off, there are two antibound state modes and one bound state mode in the singlet channel and two bound state modes in the triplet channel, while for finite values of intersite interaction two bound state modes were found in each channel. Our results for dynamical charge and spin structure factors indicate that only one of two bound/antibound state modes can be probed by electron-energy-loss spectroscopy and inelastic neutron scattering experiments.