Quantum Hall edges beyond the plasma analogy

TL;DR

This paper reveals the limitations of the plasma analogy in predicting edge properties of quantum Hall states, emphasizing fundamental differences and their impact on observable physical quantities.

Contribution

It identifies the fundamental reasons for the plasma analogy's failure at quantum Hall edges and quantifies its effects on measurable physical properties.

Findings

Plasma analogy fails at quantum Hall edges except in fine-tuned geometries.

Edge fluctuations and absorption rates are significantly affected by the analogy's failure.

Quantum Hall droplets are incompressible liquids, unlike Coulomb gases, leading to different edge behaviors.

Abstract

We demonstrate that the widely used plasma analogy is unreliable at predicting edge properties of quantum Hall states. This discrepancy arises from a fundamental difference between quantum Hall droplets and plasmas (Coulomb gases): the former are incompressible liquids subject to area-preserving deformations, while the latter are governed by electrostatics and thus involve conformal transformations. Consequently, the plasma analogy fails at the edge, except in fine-tuned geometries, as it does not account for the emergent local edge velocity. We quantitatively show how the analogy's failure affects physical quantities, such as fluctuations of local observables and absorption rates in microwave spectroscopy, measurable in both solid-state experiments and quantum simulators.