Quantum Entanglement as a Diagnostic of Phase Transitions in Disordered Fractional Quantum Hall Liquids

TL;DR

This paper uses quantum entanglement measures to identify and analyze the disorder-driven phase transition from fractional quantum Hall states to Anderson insulators, revealing a divergence in entanglement entropy sensitivity.

Contribution

It introduces entanglement entropy derivatives as a diagnostic tool for phase transitions in disordered quantum Hall systems, highlighting their divergence at the transition point.

Findings

Entanglement entropy derivative diverges at the transition.

Level statistics show gradual changes, not sharp transitions.

Entanglement measures effectively signal phase boundaries.

Abstract

We investigate the disorder-driven phase transition from a fractional quantum Hall state to an Anderson insulator using quantum entanglement methods. We find that the transition is signaled by a sharp increase in the sensitivity of a suitably averaged entanglement entropy with respect to disorder -- the magnitude of its disorder derivative appears to diverge in the thermodynamic limit. We also study the level statistics of the entanglement spectrum as a function of disorder. However, unlike the dramatic phase-transition signal in the entanglement entropy derivative, we find a gradual reduction of level repulsion only deep in the Anderson insulating phase.