Field Theoretical Description of Quantum Hall Edge Reconstruction

TL;DR

This paper generalizes the chiral Luttinger liquid theory to describe quantum Hall edges with or without reconstruction, revealing a quantum phase transition and its effects on tunneling behavior.

Contribution

It introduces a unified theoretical framework for quantum Hall edge states that includes edge reconstruction as a quantum phase transition.

Findings

Edge reconstruction is a quantum phase transition in the universality class of 1D dilute Bose gas.

Edge reconstruction modifies the tunneling exponent at principal filling factors.

Critical behavior of the transition can be obtained exactly.

Abstract

We propose a generalization of the chiral Luttinger liquid theory to allow for a unified description of quantum Hall edges with or without edge reconstruction. Within this description edge reconstruction is found to be a quantum phase transition in the universality class of one-dimensional dilute Bose gas transition, whose critical behavior can be obtained exactly. At principal filling factors $\nu=1/m$, we show the additional edge modes due to edge reconstruction modifies the point contact tunneling exponent in the low energy limit, by a small and non-universal amount.