  Recently performed resonant inelastic x-ray scattering experiment (RIXS) at
the copper L3 edge in the quasi-1D Mott insulator Sr2CuO3 has revealed a
significant dispersion of a single orbital excitation (orbiton). This large and
unexpected orbiton dispersion has been explained using the concept of
spin-orbital fractionalization in which orbiton, which is intrinsically coupled
to the spinon in this material, liberates itself from the spinon due to the
strictly 1D nature of its motion. Here we investigate this mechanism in detail
by: (i) deriving the microscopic spin-orbital superexchange model from the
charge transfer model for the CuO3 chains in Sr2CuO3, (ii) mapping the orbiton
motion in the obtained spin-orbital model into a problem of a single hole
moving in an effective half-filled antiferromagnetic chain t-J model, and (iii)
solving the latter model using the exact diagonalization and obtaining the
orbiton spectral function. Finally, the RIXS cross section is calculated based
on the obtained orbiton spectral function and compared with the RIXS
experiment.
