Charge-spin-orbital dynamics of one-dimensional two-orbital Hubbard model

We study the real-time evolution of a charge-excited state in a one-dimensional eg-orbital degenerate Hubbard model, by a time-dependent density-matrix renormalization group method. Considering a chain along the z direction, electrons hop between adjacent 3z2-r2 orbitals, while x2-y2 orbitals are localized. For the charge-excited state, a holon-doublon pair is introduced into the ground state at quarter filling. At initial time, there is no electron in a holon site, while a pair of electrons occupies 3z2-r2 orbital in a doublon site. As the time evolves, the holon motion is governed by the nearest-neighbor hopping, but the electron pair can transfer between 3z2-r2 orbital and x2-y2 orbital through the pair hopping in addition to the nearest-neighbor hopping. Thus holon and doublon propagate at different speed due to the pair hopping that is characteristic of multi-orbital systems.