Quantum Hall Edges with Hard Confinement: Exact Solution beyond Luttinger Liquid

TL;DR

This paper presents an exact solution for quantum Hall edge states with hard confinement, revealing a Jack polynomial structure and a distinct energy spectrum from traditional Luttinger liquid models.

Contribution

It provides an exact analytical description of quantum Hall edges under steep confinement, extending beyond the Luttinger liquid approximation.

Findings

Eigenstates exhibit Jack polynomial structure.

Energy spectrum differs significantly from Luttinger liquid predictions.

Solution applies to steep but weak confining potentials.

Abstract

We consider a Laughlin droplet in a confining potential which is very steep but also weak compared to the ultra-short ranged inter-particle interactions. We find that the eigenstates have a Jack polynomial structure, and have an energy spectrum which is extremely different from the well-known Luttinger liquid edge.