Pair Description of the FQHE with Application to Edge Waves

TL;DR

This paper introduces a pair-based formalism to describe edge excitations in the fractional quantum Hall effect, clarifying the role of interactions and extending the approach to Laughlin states.

Contribution

It develops a pair description framework for edge excitations in FQHE and applies it to both integer and fractional states, enhancing understanding of edge dynamics.

Findings

Identifies operators creating edge excitations at ν=1

Clarifies the role of interaction potential in long wavelength limit

Extends the pair formalism to ν=1/m Laughlin states

Abstract

Pairs of particles of definite total and relative angular momentum provide a natural description for a two dimensional electron gas in a strong magnetic field. Two body operators take a simple form when expressed in terms of pair creation and destruction operators. The pair formalism is applied to the study of edge waves excitations. For $\nu=1$ the operators which create edge excitations are identified and the role the interaction potential plays in the long wavelength limit is clarified. This picture is claimed to describe also edge excitations on the $\nu=1/m$ Laughlin states.