Entanglement entropy of integer Quantum Hall states in polygonal domains

TL;DR

This paper investigates how the entanglement entropy of integer Quantum Hall states behaves in polygonal regions, revealing angle-dependent constant terms and analyzing the entanglement spectrum's geometric dependence.

Contribution

It provides a general expression for the angle-dependent constant term in entanglement entropy for polygonal domains and interprets the spectrum's geometric dependence.

Findings

Entanglement entropy in polygonal domains includes an angle-dependent constant term.

The entanglement spectrum varies with the domain's geometry.

A simple physical interpretation of the spectrum's geometric dependence is proposed.

Abstract

The entanglement entropy of the integer Quantum Hall states satisfies the area law for smooth domains with a vanishing topological term. In this paper we consider polygonal domains for which the area law acquires a constant term that only depends on the angles of the vertices and we give a general expression for it. We study also the dependence of the entanglement spectrum on the geometry and give it a simple physical interpretation.