Entanglement entropy and multifractality at localization transitions

TL;DR

This paper explores how entanglement entropy behaves at quantum localization transitions, revealing its connection to multifractality and providing insights into critical wave function fluctuations.

Contribution

It demonstrates that multifractal analysis effectively describes entanglement entropy at localization critical points in non-interacting electronic systems.

Findings

Entanglement entropy exhibits non-analytic behavior at localization transitions.

Multifractality characterizes the fluctuations of wave functions at criticality.

Numerical simulations confirm the link between entanglement and multifractal properties.

Abstract

The von Neumann entanglement entropy is a useful measure to characterize a quantum phase transition. We investigate the non-analyticity of this entropy at disorder-dominated quantum phase transitions in non-interacting electronic systems. At these critical points, the von Neumann entropy is determined by the single particle wave function intensity which exhibits complex scale invariant fluctuations. We find that the concept of multifractality is naturally suited for studying von Neumann entropy of the critical wave functions. Our numerical simulations of the three dimensional Anderson localization transition and the integer quantum Hall plateau transition show that the entanglement at these transitions is well described using multifractal analysis.