Logarithmic Entanglement Lightcone in Many-Body Localized Systems

TL;DR

This paper investigates how local quenches in many-body localized systems lead to a logarithmic entanglement lightcone, confirming a modified Lieb-Robinson bound and revealing volume-law entanglement near the transition.

Contribution

It provides a theoretical analysis of entanglement dynamics and information propagation in many-body localized systems, including the logarithmic lightcone and orthogonality catastrophe.

Findings

Entanglement spreads logarithmically after a local quench.

Final states near the transition exhibit volume-law entanglement.

Local quenches cause exponential decay of wave-function overlap.

Abstract

We theoretically study the response of a many-body localized system to a local quench from a quantum information perspective. We find that the local quench triggers entanglement growth throughout the whole system, giving rise to a logarithmic lightcone. This saturates the modified Lieb-Robinson bound for quantum information propagation in many-body localized systems previously conjectured based on the existence of local integrals of motion. In addition, near the localization-delocalization transition, we find that the final states after the local quench exhibit volume-law entanglement. We also show that the local quench induces a deterministic orthogonality catastrophe for highly excited eigenstates, where the typical wave-function overlap between the pre- and post-quench eigenstates decays {\it exponentially} with the system size.