Geometric entanglement in integer quantum Hall states

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.

Automated summary

The study examines the quantum entanglement structure of integer quantum Hall states through the reduced density matrix of spatial subregions. It reveals geometric angle-dependent contributions and nearly identical angle dependencies to numerous conformal field theories (CFTs). Additionally, excitations localized near corners are observed in the low-lying entanglement spectrum.