Effective Edge State Dynamics in the Fractional Quantum Hall Effect

TL;DR

This paper develops effective Hamiltonians to describe quantum Hall edge states beyond the low-energy Luttinger liquid regime, accounting for bulk interactions and symmetries, enabling accurate modeling of edge physics at higher energies and smaller system sizes.

Contribution

It introduces a method to construct and constrain effective edge Hamiltonians using conformal field theory and bulk symmetries, extending the understanding of quantum Hall edges beyond traditional limits.

Findings

Simplified effective theories accurately describe edge physics away from the Luttinger liquid fixed point.

The approach applies to small systems and higher energies, broadening the scope of quantum Hall edge analysis.

Bulk symmetries significantly constrain the form of effective edge Hamiltonians.

Abstract

We consider the behaviour of quantum Hall edges away from the Luttinger liquid fixed point that occurs in the low energy, large system limit. Using the close links between quantum Hall wavefunctions and conformal field theories we construct effective Hamiltonians from general principles and then constrain their forms by considering the effect of bulk symmetries on the properties of the edge. In examining the effect of bulk interactions on this edge we find remarkable simplifications to these effective theories which allow for a very accurate description of the low-energy physics of quantum Hall edges relatively far away from the Luttinger liquid fixed point, and which apply to small systems and higher energies.