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

Dynamical simulations of charged soliton transport in conjugated polymers with the inclusion of electron-electron interactions