Excitation spectra of intertwined spin and orbital degrees of freedom*

Even without the spin-orbit coupling, spin and orbital still couple in insulating transition-metal oxides due to the superexchange. The low-energy spectrum is therefore made up not only of spin, but also orbital, and simultaneous spin-orbital excitations. All of these can now be measured owing to the advances in resonant inelastic x-ray scattering. This calls for an accurate theoretical modeling. Here, we study the excitation spectra of the spin-orbital chain (the Kugel-Khomskii model), which forms a low-energy theory of the insulating two-orbital Hubbard chain at quarter filling. We use the density-matrix renormalization group method to properly incorporate the spin-orbital fluctuations and obtain accurate spectra with high resolution. In this way, we go beyond the usual mean-field decoupling where the spin and orbital dynamics are treated as independent. We discuss the spin and orbital dynamical structure factors and comment upon the unique combined spin-orbital excitations.