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We present a generalized adaptive time-dependent density matrixrenormalization group (DMRG) scheme, called the {\it double time windowtargeting} (DTWT) technique, which gives accurate results with nominalcomputational resources, within reasonable computational time. This procedureoriginates from the amalgamation of the features of pace keeping DMRGalgorithm, first proposed by Luo {\it et. al}, [Phys.Rev. Lett. {\bf 91},049701 (2003)], and the time-step targeting (TST) algorithm by Feiguin andWhite [Phys. Rev. B {\bf 72}, 020404 (2005)]. Using the DTWT technique, westudy the phenomena of spin-charge separation in conjugated polymers (materialsfor molecular electronics and spintronics), which have long-rangeelectron-electron interactions and belong to the class of strongly correlatedlow-dimensional many-body systems. The issue of real time dynamics within thePariser-Parr-Pople (PPP) model which includes long-range electron correlationshas not been addressed in the literature so far. The present study on PPPchains has revealed that, (i) long-range electron correlations enable both thecharge and spin degree of freedom of the electron, to propagate faster in thePPP model compared to Hubbard model, (ii) for standard parameters of the PPPmodel as applied to conjugated polymers, the charge velocity is almost twicethat of the spin velocity and, (iii) the simplistic interpretation oflong-range correlations by merely renormalizing the {\it U} value of theHubbard model fails to explain the dynamics of doped holes/electrons in the PPPmodel.

Double Time Window Targeting Technique: Real time DMRG dynamics in the PPP model