Geometric entanglement in integer quantum Hall states with boundaries

TL;DR

This paper investigates how boundaries affect entanglement properties in integer quantum Hall states, revealing boundary-induced contributions and their geometric dependence, with implications for topological and critical systems.

Contribution

It provides a detailed analysis of boundary and corner effects on entanglement entropy in quantum Hall systems, including angle dependence and spatial structure insights.

Findings

Entanglement entropy includes a boundary corner contribution.

The corner term's angle dependence is characterized.

Boundary effects influence the reduced density matrix structure.

Abstract

Boundaries constitute a rich playground for quantum many-body systems because they can lead to novel degrees of freedom such as protected boundary states in topological phases. Here, we study the groundstate of integer quantum Hall systems in the presence of boundaries through the reduced density matrix of a spatial region. We work in the lowest Landau level and choose our region to intersect the boundary at arbitrary angles. The entanglement entropy (EE) contains a logarithmic contribution coming from the chiral edge modes, and matches the corresponding conformal field theory prediction. We uncover an additional contribution due to the boundary corners. We characterize the angle-dependence of this boundary corner term, and compare it to the bulk corner EE. We further analyze the spatial structure of entanglement via the eigenstates associated with the reduced density matrix, and construct a spatially-resolved EE. The influence of the physical boundary and the region's geometry on the reduced density matrix is thus clarified. Finally, we discuss the implications of our findings for other topological phases, as well as quantum critical systems such as conformal field theories in 2 spatial dimensions.