Bulk-Boundary Correspondence in the Quantum Hall Effect

TL;DR

This paper provides a microscopic analysis of edge excitations in the quantum Hall effect, clarifying the role of orbital spin and its universal features, and extends the understanding to fractional fillings using symmetry considerations.

Contribution

It introduces a detailed microscopic approach to edge states, highlighting the significance of orbital spin and its universal behavior, and generalizes results to fractional quantum Hall states.

Findings

Orbital spin s_i influences edge conformal field theory.

Orbital spin s_i causes observable Casimir or chemical potential shifts.

Results extend to fractional and hierarchical quantum Hall states.

Abstract

We present a detailed microscopic study of edge excitations for n filled Landau levels. We show that the higher-level wavefunctions possess a non-trivial radial dependence that should be integrated over for properly defining the edge conformal field theory. This analysis let us clarify the role of the electron orbital spin s in the edge theory and to discuss its universality, thus providing a further instance of the bulk-boundary correspondence. We find that the values s_i for each level, i=1,...,n, parameterize a Casimir effect or chemical potential shift that could be experimentally observed. These results are generalized to fractional and hierarchical fillings by exploiting the W-infinity symmetry of incompressible Hall fluids.