Local entanglement structure across a many-body localization transition

TL;DR

This study examines how local entanglement, measured by concurrence, changes across a many-body localization transition in a disordered spin system, revealing a clear shift from zero to nonzero concurrence and its correlation with spectral statistics.

Contribution

It demonstrates that local concurrence serves as an indicator of the many-body localization transition and correlates with spectral and disorder properties, providing new insights into entanglement behavior in disordered systems.

Findings

Concurrence vanishes in the ergodic phase and becomes nonzero in the localized phase.

A scaling form exists in the second derivative of concurrence with respect to disorder.

Concurrence decays exponentially with distance in the localized phase.

Abstract

Local entanglement between pairs of spins, as measured by concurrence, is investigated in a disordered spin model that displays a transition from an ergodic to a many-body localized phase in excited states. It is shown that the concurrence vanishes in the ergodic phase and becomes nonzero and increases in the many-body localized phase. This happen to be correlated with the transition in the spectral statistics from Wigner to Poissonian distribution. A scaling form is found to exist in the second derivative of the concurrence with the disorder strength. It also displays a critical value for the localization transition that is close to what is known in the literature from other measures. An exponential decay of concurrence with distance between spins is observed in the localized phase. Nearest neighbor spin concurrence in this phase is also found to be strongly correlated with the disorder configuration of onsite fields: nearly similar fields implying larger entanglement.