Initial State Dependent Dynamics Across Many-body Localization Transition

Y. Prasad; Arti Garg

doi:10.1103/PhysRevB.105.214202

paper

Initial State Dependent Dynamics Across Many-body Localization Transition

arXiv:2202.05217 · doi:10.1103/PhysRevB.105.214202

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, $N_{k ink s}$ , in the density profile. On the delocalized side of the MBL transition the dynamics becomes faster with increase in $N_{k ink s}$ such that the decay exponent, $γ$ , in the density imbalance increases with increase in $N_{k ink s}$ . The growth exponent of the mean square displacement which shows a power-law behaviour $⟨ x^{2} (t)⟩ \sim t^{β}$ in the long time limit is much larger than the exponent $γ$ for 1-kink and other low kink states though $β \sim 2 γ$ for a charge density wave state. As the disorder strength increases $γ_{N_{k ink}} \to 0$ at some critical disorder, $h_{N_{k ink s}}$ which is a monotonically increasing function of $N_{k ink s}$ . A 1-kink state always underestimates the value of disorder at which the MBL transition takes place but $h_{1 - k ink}$ 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 $a ln (V t)$ not only in the MBL phase but also in the delocalised phase and in both the phases the coefficient $a$ increases with $N_{k ink s}$ 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.

arXiv comment14 pages, 12 figures

Initial State Dependent Dynamics Across Many-body Localization Transition

Abstract

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