Luttinger States at the Edge

TL;DR

This paper derives an effective Luttinger model for edge excitations in the fractional quantum Hall effect, linking bulk wavefunctions to edge states and identifying edge electrons with Luttinger hyper-fermions.

Contribution

It introduces a novel approach to model edge states using a dimensionally reduced wavefunction and identifies edge electrons with non-backscattering Bogoliubov quasi-particles.

Findings

Edge excitations modeled by a Luttinger hyper-fermion operator

Edge-electron propagator calculated from effective wavefunction

Connection established between bulk wavefunction and edge Luttinger model

Abstract

An effective wavefunction for the edge excitations in the Fractional quantum Hall effect can be found by dimensionally reducing the bulk wavefunction. Treated this way the Laughlin $\nu=1/(2n+1)$ wavefunction yields a Luttinger model ground state. We identify the edge-electron field with a Luttinger hyper-fermion operator, and the edge electron itself with a non-backscattering Bogoliubov quasi-particle. The edge-electron propagator may be calculated directly from the effective wavefunction using the properties of a one-dimensional one-component plasma, provided a prescription is adopted which is sensitive to the extra flux attached to the electrons.