Initial State Dependent Dynamics Across Many-body Localization Transition

We investigate quench dynamics across many-body localization (MBL) transition in an interacting one dimensional system of spinless fermions with aperiodic potential. We consider a large number of initial states characterized by the number of kinks, $N_{kinks}$, in the density profile. On the delocalized side of the MBL transition the dynamics becomes faster with increase in $N_{kinks}$ such that the decay exponent, $\gamma$, in the density imbalance increases with increase in $N_{kinks}$. The growth exponent of the mean square displacement which shows a power-law behaviour $\langle x^2(t) \rangle \sim t^\beta$ in the long time limit is much larger than the exponent $\gamma$ for 1-kink and other low kink states though $\beta \sim 2\gamma$ for a charge density wave state. As the disorder strength increases $\gamma_{N_{kink}} \rightarrow 0$ at some critical disorder, $h_{N_{kinks}}$ which is a monotonically increasing function of $N_{kinks}$. A 1-kink state always underestimates the value of disorder at which the MBL transition takes place but $h_{1-kink}$ coincides with the onset of the sub-diffusive phase preceding the MBL phase. This is consistent with the dynamics of interface broadening for the 1-kink state. We show that the bipartite entanglement entropy has a logarithmic growth $a \ln(Vt)$ not only in the MBL phase but also in the delocalised phase and in both the phases the coefficient $a$ increases with $N_{kinks}$ as well as with the interaction strength $V$. We explain this dependence of dynamics on the number of kinks in terms of the normalized participation ratio of initial states in the eigenbasis of the interacting Hamiltonian.