Fractional statistics and duality: strong tunneling behavior of edge states of quantum Hall liquids in the Jain sequence

TL;DR

This paper develops a duality framework for edge states in Jain sequence fractional quantum Hall systems, revealing how fractional statistics influence tunneling behavior and the transition to strong coupling regimes.

Contribution

It introduces a weak-strong coupling duality for FQH edge states in the Jain sequence, accounting for fractional statistics and edge reconstruction effects.

Findings

Duality relates weak and strong tunneling regimes in Jain sequence FQH states.

Fractional statistics lead to additional phase factors in tunneling processes.

Duality applies to both simple and weakly reconstructed edges.

Abstract

While the values for the fractional charge and fractional statistics coincide for fractional Hall (FQH) states in the Laughlin sequence, they do not for more general FQH states, such as those in the Jain sequence. This mismatch leads to additional phase factors in the weak coupling expansion for tunneling between edge states which alter the nature of the strong tunneling limit. We show here how to construct a weak-strong coupling duality for generalized FQH states with simple unreconstructed edges. The correct dualization of quasiparticles into integer charged fermions is a consistency requirement for a theory of FQH edge states with a simple edge. We show that this duality also applies for weakly reconstructed edges.