Bulk Versus Edge in the Quantum Hall Effect

TL;DR

This paper discusses the fundamental relationship between the bulk quantum Hall effect and its edge manifestation, emphasizing the role of the chiral anomaly as the core principle of the edge approach.

Contribution

It clarifies the conceptual foundation of the edge approach by linking the chiral anomaly to the quantum Hall effect's edge phenomena.

Findings

The chiral anomaly underpins the edge approach to quantum Hall effect.

$\sxy$ should not be interpreted as conductance from the edge current correlation.

The bulk-edge relationship is fundamentally rooted in the chiral anomaly.

Abstract

The manifestation of the bulk quantum Hall effect on edge is the chiral anomaly. The chiral anomaly {\it is} the underlying principle of the ``edge approach'' of quantum Hall effect. In that approach, $\sxy$ should not be taken as the conductance derived from the space-local current-current correlation function of the pure one-dimensional edge problem.