Entanglement entropy for integer quantum Hall effect in two and higher dimensions

TL;DR

This paper investigates the entanglement entropy in higher-dimensional integer quantum Hall systems on complex projective spaces, revealing universal proportionality to phase-space area and differences in eigenfunction profiles across Landau levels.

Contribution

It provides a semiclassical calculation of entanglement entropy in higher dimensions and identifies universal behavior and eigenfunction profile features.

Findings

Entropy proportional to phase-space area at ν=1

Universal proportionality constant across dimensions and backgrounds

Distinct eigenfunction profiles differentiate Landau levels

Abstract

We analyze the entanglement entropy, in real space, for the higher dimensional integer quantum Hall effect on ${\mathbb {CP}}^k$ (any even dimension) for abelian and nonabelian magnetic background fields. In the case of $\nu=1$ we perform a semiclassical calculation which gives the entropy as proportional to the phase-space area. This exhibits a certain universality in the sense that the proportionality constant is the same for any dimension and for any background, abelian or nonabelian. We also point out some distinct features in the profiles of the eigenfunctions of the two-point correlator that underline the difference in the value of entropies between $\nu=1$ and higher Landau levels.