Stability of Chiral Luttinger Liquids and Abelian Quantum Hall States.

TL;DR

This paper establishes a criterion for the topological stability of Abelian quantum Hall states and boundary Luttinger liquids, and analyzes their electromagnetic response, including quantized Hall conductance.

Contribution

It introduces a stability criterion for Abelian quantum Hall states and boundary Luttinger liquids, and describes their electromagnetic response properties.

Findings

Topological stability criterion for Abelian quantum Hall states.

Hall conductance is quantized regardless of edge mode directions.

A selection rule for states in the quantum Hall hierarchy.

Abstract

A criterion is given for topological stability of Abelian quantum Hall states, and of Luttinger liquids at the boundaries between such states; this suggests a selection rule on states in the quantum Hall hierarchy theory. The linear response of Luttinger liquids to electromagnetic fields is described: the Hall conductance is quantized, irrespective of whether edge modes propagate in different directions.