Entanglement entropy of integer Quantum Hall states

TL;DR

This paper calculates the real-space entanglement entropy of integer Quantum Hall states across different geometries, confirming the area law and showing the entropy per perimeter length depends on filling fraction but not on shape.

Contribution

It provides a detailed analysis of entanglement entropy in integer Quantum Hall states across multiple geometries, confirming the area law and independence from geometry.

Findings

Entanglement entropy follows the area law with zero topological entanglement entropy.

Entropy per unit length depends on filling fraction.

Entropy is independent of the domain's geometry.

Abstract

We compute the entanglement entropy, in real space, of the ground state of the integer Quantum Hall states for three different domains embedded in the torus, the disk and the sphere. We establish the validity of the area law with a vanishing value of the topological entanglement entropy. The entropy per unit length of the perimeter depends on the filling fraction, but it is independent of the geometry.