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We investigate the effect of static electron-phonon coupling, on real-timedynamics of spin and charge transport in $\pi$-conjugated polyene chains. Thepolyene chain is modeled by the Pariser-Parr-Pople Hamiltonian with dimerizednearest-neighbor parameter $t_{0}(1+\delta)$ for short bonds and$t_{0}(1-\delta)$ for long bonds, and long-range electron-electroninteractions. We follow the time evolution of the spin and charge usingtime-dependent density matrix renormalization group technique, when a hole isinjected at one end of the chain in its ground state. We find that spin andcharge dynamics followed through spin and charge velocities, depend both onchain length and extent of dimerization, $\delta$. Analysis of the resultsrequires focusing on physical quantities such as average spin and chargepolarizations, particularly in the large dimerization limit. In thedimerization range 0.0 $\le$ $\delta$ $\le$ 0.15, spin-charge dynamics is foundto have a well defined behavior, with spin-charge separation (measured as theratio of charge velocity to spin velocity) as well as, the total amount ofcharge and spin transported in a given time, along the chain, decreasing asdimerization increases. However, in the range 0.3 $\le$ $\delta$ $\le$ 0.5, itis observed that the dynamics of spin and charge transport becomes complicated.It is observed that for large $\delta$ values, spin-charge separation issuppressed and the injected hole fails to travel the entire length of thechain.

physical review. b, condensed matter and materials physics

Effect of dimerization on dynamics of spin-charge separation in  Pariser-Parr-Pople model: A time-dependent density matrix renormalization  group study