The entanglement entropy of the quantum Hall edge and its geometric contribution

TL;DR

This paper investigates the entanglement entropy in quantum Hall systems, revealing geometric and edge contributions consistent with conformal field theory and recent fluctuation studies, highlighting universal behaviors in topological phases.

Contribution

It provides a unified analysis of geometric and edge contributions to entanglement entropy in quantum Hall states, including edge reconstruction effects.

Findings

Scaling matches conformal field theory predictions

Edge reconstruction influences entanglement entropy

Universal angle-dependent geometric contributions identified

Abstract

Generally speaking, the entanglement entropy (EE) between two subregions of a gapped quantum many-body state is proportional to the area/length of their interface due to the short range quantum correlation. However, the so-called area law is violated logarithmically in a quantum critical phase. Moreover, the subleading correction exists in a long range entangled topological phases. It is referred to as topological EE which is related to the quantum dimension of the collective excitation in the bulk. Further more, if a non-smooth sharp angle is in the presence of the subsystem boundary, a universal angle dependent geometric contribution is expected to appear in the subleading correction. In this work, we simultaneously explore the geometric and edge contribution in the integer quantum Hall (IQH) state and its edge reconstruction in a unified bipartite method. Their scaling is found to be consistent with the conformal field theory (CFT) predictions and recent results of the particle number fluctuation calculations.