Double occupancies in confined attractive fermions on optical lattices

We perform a numerical study of a one-dimensional Fermi-Hubbard model in harmonic traps within the Thomas-Fermi approximation based on the exact Bethe-ansatz solution. The rho-U/t phase diagram is shown for the systems of attractive interactions (rho is the characteristic density and U/t the interaction strength scaled in units of the hopping parameter). We study the double occupancy, the local central density, and their derivatives. Their roles in detecting the composite phases induced by the trapping potential are discussed in detail.