  Recent angle-resolved photoemission spectroscopy (ARPES) for a newly
discovered doped one-dimensional (1D) Mott insulator
Ba$_{2-x}$Sr$_x$CuO$_{3+\delta}$ proposed the presence of attractive charge
interactions between neighboring sites if an 1D Hubbard model is employed to
describe the material. On the other hand, long-range repulsive charge
interactions were proposed to be crucial for understanding optical excitations
of undoped 1D Mott insulators. Motivated by these contrasting proposals, we
perform density-matrix renormalization group calculations of the
single-particle spectral function as well as dynamical spin and charge
structure factors for two kinds of extended 1D Hubbard models. The spectral
function for the long-range repulsive model less agrees with the ARPES data as
compared with that for the attractive one. The dynamical spin and charge
structure factors also exhibit contrasting behaviors between the two models:
the attractive model shows less momentum dependence of the integrated weight in
the dynamical spin structure factor and more accumulation of the weight on the
upper edge of particle-hole-type excitation in the dynamical charge structure
factor. These features give a good criterion of an appropriate model for doped
1D Mott insulators, which can be judged by resonant-inelastic x-ray scattering
experiments.
