Flow equations for the ionic Hubbard model

Taking the site-diagonal terms of the ionic Hubbard model (IHM) in one and two spatial dimensions, as H0H0, 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 Δ, 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=Uc1U=Uc1, where spin and charge gaps both vanish and remain zero up to U=Uc2U=Uc2. A gap-less state in charge and spin sectors characterizes a metal. For U>Uc2U>Uc2 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.