  Motivated by experimental developments introducing the concept of spin-orbit
separation, we study the real-space time evolution of an excitonic wave-packet
using a two-orbital Hubbard model. The exciton is created by exciting an
electron from a lower energy half-filled orbital to a higher energy empty
orbital. We carry out the real-time dynamics of the resulting excitonic
wave-packet, using the time-dependent density matrix renormalization group
method. We find clear evidence of charge-spin and spin-orbit separation in
real-space, by tracking the time evolution of local observables. We show that
the velocity of the orbiton can be tuned by varying the inter-orbital
interactions. We also present a comparative study of a hole (in one orbital)
and exciton (in two orbitals) dynamics in one-dimensional systems. Moreover, we
analyze the dynamics of an exciton with spin-flip excitation, where we observe
fractionalized spinons induced by Hund's interaction.
