Effects of disorder on atomic density waves and spin-singlet dimers in one-dimensional optical lattices

Using the Bethe-ansatz density-functional theory, we study a one-dimensional Hubbard model of confined attractively interacting fermions in the presence of a uniformly distributed disorder. The strongly-correlated Luther-Emery nature of the attractive one-dimensional Hubbard model is fully taken into account as the reference system in the density-functional theory. The effects of the disorder are investigated on the atomic-density waves in the weak-to-intermediate attractive interaction and on the spin-singlet dimers of doubly occupied sites in the strongly attractive regime. It is found that atomic density waves are sensitive to the disorder and the spin-singlet dimers of doubly occupied sites are quite unstable against the disorder. We also show that very weak disorder could smear the singularities in the stiffness, thus suppress the spin-singlet pairs.