Universal structure of the edge states of the fractional quantum Hall states

TL;DR

This paper develops a universal effective theory for the edge states of fractional quantum Hall states on closed surfaces, revealing a common structure across different fractions and detailing the properties of edge excitations and tunneling behavior.

Contribution

It introduces a universal form of the effective theory for Jain sequence fractional quantum Hall states, derived from flux attachment consistency, and characterizes the edge states with a single propagating mode and topological fields.

Findings

Edge states for all Jain fractions have one propagating mode carrying charge and energy.

Two non-propagating topological edge fields determine excitation statistics.

Tunneling density of states scales as ||^{(1- u)/ u} for all Jain states.

Abstract

We present an effective theory for the bulk fractional quantum Hall states on the Jain sequences on closed surfaces and show that it has a universal form whose structure does not change from fraction to fraction. The structure of this effective theory follows from the condition of global consistency of the flux attachment transformation on closed surfaces. We derive the theory of the edge states on a disk that follows naturally from this globally consistent theory on a torus. We find that, for a fully polarized two-dimensional electron gas, the edge states for all the Jain filling fractions $\nu=p/(2np+1)$ have only one propagating edge field that carries both energy and charge, and two non-propagating edge fields of topological origin that are responsible for the statistics of the excitations. Explicit results are derived for the electron and quasiparticle operators and for their propagators at the edge. We show that these operators create states with the correct charge and statistics. It is found that the tunneling density of states for all the Jain states scales with frequency as $|\omega|^{(1-\nu)/\nu}$.