  Dynamical simulations of polaron transport in conjugated polymers in the
presence of an external time-dependent electric field have been performed
within a combined extended Hubbard model (EHM) and Su-Schrieffer-Heeger (SSH)
model. Nearly all relevant electron-phonon and electron-electron interactions
are fully taken into account by solving the time-dependent Schr\"{o}dinger
equation for the $\pi$-electrons and the Newton's equation of motion for the
backbone monomer displacements by virtue of the combination of the adaptive
time-dependent density matrix renormalization group (TDDMRG) and classical
molecular dynamics (MD). We find that after a smooth turn-on of the external
electric field the polaron is accelerated at first and then moves with a nearly
constant velocity as one entity consisting of both the charge and the lattice
deformation. An ohmic region (3 mV/$\text{\AA}$ $\leq E_0\leq$ 9
mV/$\text{\AA}$) where the stationary velocity increases linearly with the
electric field strength is observed for the case of $U$=2.0 eV and $V$=1.0 eV.
The maximal velocity is well above the speed of sound. Below 3 mV/$\text{\AA}$
the polaron velocity increases nonlinearly and in high electric fields with
strength $E_0\geq$ 10.0 mV/$\text{\AA}$ the polaron will become unstable and
dissociate. The relationship between electron-electron interaction strengths
and polaron transport is also studied in detail. We find that the the on-site
Coulomb interactions $U$ will suppress the polaron transport and small
nearest-neighbor interactions $V$ values are also not beneficial to the
polaronic motion while large $V$ values favor the polaron transport.
