Signatures of the many-body localization transition in the dynamics of entanglement and bipartite fluctuations

TL;DR

This paper investigates the many-body localization transition in the XXZ model by analyzing entanglement and bipartite fluctuations after a quantum quench, revealing divergence-like behavior near the transition.

Contribution

It demonstrates the relevance of entanglement and bipartite fluctuations as indicators of the localization transition, highlighting their divergent behavior at criticality.

Findings

Long-time limits of entanglement and fluctuations show divergence near the transition.

Behavior of these quantities provides insights into the nature of the localization transition.

Results suggest these measures can serve as signatures of the transition.

Abstract

The many-body localization transition is a dynamical quantum phase transition between a localized and an extended phase. We study this transition in the XXZ model with disordered magnetic field and focus on the time evolution following a global quantum quench. While the dynamics of the bipartite entanglement and spin fluctuations are already known to provide insights into the nature of the many-body localized phases, we discuss the relevance of these quantities in the context of the localization transition. In particular, we observe that near the transition the long time limits of both quantities show behavior similar to divergent thermodynamic fluctuations.