Edge States and Entanglement Entropy

TL;DR

This paper explores how boundary-localized gauge field states contribute to entanglement entropy, showing that for the quantum Hall effect, the entropy follows an approximate area law due to coarse-graining.

Contribution

It demonstrates how boundary states in gauge fields lead to entanglement entropy and connects this to the area law in the quantum Hall effect.

Findings

Boundary states support localized states at manifolds' edges.

Coarse-graining over boundary states yields entanglement entropy.

Quantum Hall ground state entropy approximately follows an area law.

Abstract

It is known that gauge fields defined on manifolds with spatial boundaries support states localized at the boundaries. In this paper, we demonstrate how coarse-graining over these states can lead to an entanglement entropy. In particular, we show that the entanglement entropy of the ground state for the quantum Hall effect on a disk exhibits an approximate ``area " law.