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We investigate quench dynamics across many-body localization (MBL) transitionin an interacting one dimensional system of spinless fermions with aperiodicpotential. We consider a large number of initial states characterized by thenumber of kinks, $N_{kinks}$, in the density profile. On the delocalized sideof the MBL transition the dynamics becomes faster with increase in $N_{kinks}$such that the decay exponent, $\gamma$, in the density imbalance increases withincrease in $N_{kinks}$. The growth exponent of the mean square displacementwhich shows a power-law behaviour $\langle x^2(t) \rangle \sim t^\beta$ in thelong time limit is much larger than the exponent $\gamma$ for 1-kink and otherlow kink states though $\beta \sim 2\gamma$ for a charge density wave state. Asthe disorder strength increases $\gamma_{N_{kink}} \rightarrow 0$ at somecritical disorder, $h_{N_{kinks}}$ which is a monotonically increasing functionof $N_{kinks}$. A 1-kink state always underestimates the value of disorder atwhich the MBL transition takes place but $h_{1-kink}$ coincides with the onsetof the sub-diffusive phase preceding the MBL phase. This is consistent with thedynamics of interface broadening for the 1-kink state. We show that thebipartite entanglement entropy has a logarithmic growth $a \ln(Vt)$ not only inthe MBL phase but also in the delocalised phase and in both the phases thecoefficient $a$ increases with $N_{kinks}$ as well as with the interactionstrength $V$. We explain this dependence of dynamics on the number of kinks interms of the normalized participation ratio of initial states in the eigenbasisof the interacting Hamiltonian.

Initial State Dependent Dynamics Across Many-body Localization Transition