Initial state dependent dynamics across the many-body localization transition

Abstract

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 ${N}_{\mathrm{kinks}}$ in the density profile, such that the equal number of sites are occupied between any two consecutive kinks. We show that on the delocalized side of the MBL transition the dynamics becomes faster with increase in ${N}_{\mathrm{kinks}}$ such that the decay exponent $\ensuremath{\gamma}$ in the density imbalance increases with increase in ${N}_{\mathrm{kinks}}$. The growth exponent of the mean square displacement which shows a power-law behavior $\ensuremath{\langle}{x}^{2}(t)\ensuremath{\rangle}\ensuremath{\sim}{t}^{\ensuremath{\beta}}$ in the long-time limit is much larger than the exponent $\ensuremath{\gamma}$ for one-kink and other low-kink states though $\ensuremath{\beta}\ensuremath{\sim}2\ensuremath{\gamma}$ for a charge density wave state. As the disorder strength increases ${\ensuremath{\gamma}}_{{N}_{\mathrm{kink}}}\ensuremath{\rightarrow}0$ at some critical disorder, ${h}_{{N}_{\mathrm{kinks}}}$, which is a monotonically increasing function of ${N}_{\mathrm{kinks}}$. A one-kink state always underestimates the value of the disorder at which the MBL transition takes place but ${h}_{\text{1}\phantom{\rule{0.16em}{0ex}}\text{kink}}$ coincides with the onset of the subdiffusive phase preceding the MBL phase. This is consistent with the dynamics of interface broadening for the one-kink state. We show that the bipartite entanglement entropy has a logarithmic growth $aln(Vt)$ not only in the MBL phase but also in the delocalized phase and in both the phases the coefficient $a$ increases with ${N}_{\mathrm{kinks}}$ 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.