Entanglement contour perspective for strong area law violation in a disordered long-range hopping model

TL;DR

This paper explores how entanglement and localization properties in a disordered long-range hopping model relate to area-law violations, revealing signatures of phase transitions through entanglement and fluctuation contours.

Contribution

It introduces the entanglement contour perspective to explain area-law violations and links entanglement, fluctuations, and phase transitions in disordered long-range systems.

Findings

Delocalized phase exhibits strong area-law violation.

Localized phases follow the strict area law for large subsystems.

Entanglement and fluctuation contours reveal transition signatures.

Abstract

We numerically investigate the link between the delocalization-localization transition and entanglement in a disordered long-range hopping model of spinless fermions by studying various static and dynamical quantities. This includes the inverse participation ratio, level-statistics, entanglement entropy and number fluctuations in the subsystem along with quench and wave-packet dynamics. Finite systems show delocalized, quasi-localized and localized phases. The delocalized phase shows strong area-law violation whereas the (quasi)localized phase adheres to (for large subsystems) the strict area law. The idea of `entanglement contour' nicely explains the violation of area-law and its relationship with `fluctuation contour' reveals a signature at the transition point. The relationship between entanglement entropy and number fluctuations in the subsystem also carries signatures for the transition in the model. Results from Aubry-Andre-Harper model are compared in this context. The propagation of charge and entanglement are contrasted by studying quench and wavepacket dynamics at the single-particle and many-particle levels.