Entanglement spectroscopy of chiral edge modes in the Quantum Hall effect

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.