Scrambling and Many-Body Localization in the XXZ-Chain

TL;DR

This paper investigates the tripartite information as an observable-independent measure to distinguish many-body localized from delocalized regimes in the XXZ-chain, revealing logarithmic spreading and disorder suppression effects.

Contribution

It demonstrates that tripartite information effectively indicates many-body localization and delocalization, with detailed analysis of its spreading and saturation behavior in the XXZ-chain.

Findings

Tripartite information spreads logarithmically in the MBL regime.

The tripartite information reaches a disorder-suppressed plateau.

The measure is observable-independent and effective for distinguishing regimes.

Abstract

The tripartite information is an observable-independent measure for scrambling and delocalization of information. Therefore one can expect that the tripartite information is a good observable-independent indicator for distinguishing between many-body localized and delocalized regimes, which we confirm for the XXZ-chain in a random field. Specifically, we find that the tripartite information signal spreads inside a lightcone that only grows logarithmically in time in the many-body localized regime similar to the entanglement entropy. We also find that the tripartite information eventually reaches a plateau with an asymptotic value that is suppressed by strong disorder.