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

We investigate the effect of static electron-phonon coupling, on real-time dynamics of spin and charge transport in $π$-conjugated polyene chains. The polyene chain is modeled by the Pariser-Parr-Pople Hamiltonian with dimerized nearest-neighbor parameter $t_{0}(1+δ)$ for short bonds and $t_{0}(1-δ)$ for long bonds, and long-range electron-electron interactions. We follow the time evolution of the spin and charge using time-dependent density matrix renormalization group technique, when a hole is injected at one end of the chain in its ground state. We find that spin and charge dynamics followed through spin and charge velocities, depend both on chain length and extent of dimerization, $δ$. Analysis of the results requires focusing on physical quantities such as average spin and charge polarizations, particularly in the large dimerization limit. In the dimerization range 0.0 $\le$ $δ$ $\le$ 0.15, spin-charge dynamics is found to have a well defined behavior, with spin-charge separation (measured as the ratio of charge velocity to spin velocity) as well as, the total amount of charge and spin transported in a given time, along the chain, decreasing as dimerization increases. However, in the range 0.3 $\le$ $δ$ $\le$ 0.5, it is observed that the dynamics of spin and charge transport becomes complicated. It is observed that for large $δ$ values, spin-charge separation is suppressed and the injected hole fails to travel the entire length of the chain.