Topological orders and Edge excitations in FQH states

TL;DR

This paper explores the complex topological orders in fractional quantum Hall liquids and how edge excitations, modeled as chiral Luttinger liquids, serve as practical probes for these orders.

Contribution

It provides a classification of topological orders in FQH states and links edge excitations to the bulk topological properties.

Findings

Edge excitations form chiral Luttinger liquids reflecting bulk topological order

Edge excitations can be used to experimentally measure topological orders

Rich structures of edge states mirror the internal order of FQH liquids

Abstract

Fractional quantum Hall (FQH) liquids contain extremely rich internal structures which represent a whole new kind of ordering. We discuss characterization and classification of the new orders (which is called topological orders). We also discuss the edge excitations in FQH liquids, which form the so-called chiral Luttinger liquids. The chiral Luttinger liquids at the edges also have very rich structures as a reflection of the rich topological orders in the bulk. Thus, edge excitations provide us a practical way to measure topological orders in experiments.