Entanglement spectroscopy of chiral edge modes in the Quantum Hall effect

TL;DR

This paper calculates the entanglement entropy in the Integer Quantum Hall effect, showing it matches that of a chiral Dirac fermion and persists in interacting systems, revealing details about edge states and their properties.

Contribution

It provides an exact microscopic calculation of entanglement entropy in Quantum Hall systems, including interactions, linking it to edge modes and conformal field theory.

Findings

Edge entanglement entropy matches chiral Dirac fermion predictions

Conformal formula with central charges c+bar{c}=1 is recovered

Behavior persists in strongly interacting Laughlin liquids

Abstract

We investigate the entanglement entropy in the Integer Quantum Hall effect in the presence of an edge, performing an exact calculation directly from the microscopic two-dimensional wavefunction. The edge contribution is shown to coincide exactly with that of a chiral Dirac fermion, and this correspondence holds for an arbitrary collection of intervals. In particular for a single interval the celebrated conformal formula is recovered with left and right central charges $c+\bar{c} =1$. Using Monte-Carlo techniques we establish that this behavior persists for strongly interacting systems such as Laughlin liquids. This illustrates how entanglement entropy is not only capable of detecting the presence of massless degrees of freedom, but also of pinpointing their position in real space, as well as elucidating their nature.