Geometric entanglement in integer quantum Hall states

TL;DR

This paper investigates the entanglement properties of integer quantum Hall states, revealing geometric and conformal field theory connections, and explores implications for fractional states.

Contribution

It uncovers the angle-dependent corner contributions to entanglement entropy and their relation to conformal field theories in quantum Hall states.

Findings

Corner entanglement entropy exhibits angle dependence similar to 2D CFTs.

Corner terms obey bounds known from conformal field theories.

Low-lying entanglement spectrum shows localized excitations near corners.

Abstract

We study the quantum entanglement structure of integer quantum Hall states via the reduced density matrix of spatial subregions. In particular, we examine the eigenstates, spectrum and entanglement entropy (EE) of the density matrix for various ground and excited states, with or without mass anisotropy. We focus on an important class of regions that contain sharp corners or cusps, leading to a geometric angle-dependent contribution to the EE. We unravel surprising relations by comparing this corner term at different fillings. We further find that the corner term, when properly normalized, has nearly the same angle dependence as numerous conformal field theories (CFTs) in two spatial dimensions, which hints at a broader structure. In fact, the Hall corner term is found to obey bounds that were previously obtained for CFTs. In addition, the low-lying entanglement spectrum and the corresponding eigenfunctions reveal "excitations" localized near corners. Finally, we present an outlook for fractional quantum Hall states.