Initial State Dependent Dynamics Across Many-body Localization Transition

TL;DR

This study explores how initial state configurations influence the dynamics of many-body localization transitions in a one-dimensional fermionic system, revealing dependence of transition points and entanglement growth on initial kink states.

Contribution

It introduces a detailed analysis of initial state dependence in MBL dynamics, linking kink number to transition points, entanglement growth, and participation ratios, advancing understanding of non-equilibrium quantum phases.

Findings

Higher kink states lead to faster dynamics on the delocalized side.

Disorder strength at transition increases with initial kink number.

Logarithmic entanglement growth occurs in both phases, with coefficient depending on initial state.

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, $N_{kinks}$, 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.