Out-of-Time-Order Correlation in Marginal Many-Body Localized Systems

TL;DR

This paper demonstrates that the out-of-time-order correlation in marginal many-body localized systems exhibits stretched exponential scrambling times, revealing Sinai diffusion and enhanced quantum information scrambling due to quantum criticality.

Contribution

It introduces an efficient method to compute OTOC in MBL systems and uncovers the stretched exponential scrambling behavior in marginal MBL systems.

Findings

OTOC can be efficiently calculated using spectrum bifurcation renormalization group.

Scrambling time scales as a stretched exponential with distance.

Quantum criticality enhances information scrambling in non-chaotic systems.

Abstract

We show that the out-of-time-order correlation (OTOC) $ \langle W(t)^\dagger V(0)^\dagger W(t)V(0)\rangle$ in many-body localized (MBL) and marginal MBL systems can be efficiently calculated by the spectrum bifurcation renormalization group (SBRG). We find that in marginal MBL systems, the scrambling time $t_\text{scr}$ follows a stretched exponential scaling with the distance $d_{WV}$ between the operators $W$ and $V$: $t_\text{scr}\sim\exp(\sqrt{d_{WV}/l_0})$, which demonstrates Sinai diffusion of quantum information and the enhanced scrambling by the quantum criticality in non-chaotic systems.