  We present numerical studies of the transport dynamics of a charged soliton
in conjugated polymers under the influence of an external time-dependent
electric field. All relevant electron-phonon and electron-electron interactions
are nearly fully taken into account by simulating the monomer displacements
with classical molecular dynamics (MD) and evolving the wavefunction for the
$\pi$ electrons by virtue of the adaptive time-dependent density matrix
renormalization group (TDDMRG) simultaneously and nonadiabatically. It is found
that after a smooth turn-on of the external electric field the charged soliton
is accelerated at first up to a stationary constant velocity as one entity
consisting of both the charge and the lattice deformation. An ohmic region (6
mV/$\text{\AA}$ $\leq E_0\leq$ 12 mV/$\text{\AA}$) where the stationary
velocity increases linearly with the electric field strength is observed. The
relationship between electron-electron interactions and charged soliton
transport is also investigated in detail. We find that the dependence of the
stationary velocity of a charged soliton on the on-site Coulomb interactions
$U$ and the nearest-neighbor interactions $V$ is due to the extent of
delocalization of the charged soliton defect.
