Symmetry Aspects and Finite-Size Scaling of Quantum Hall Fluids

TL;DR

This paper reviews how infinite $W_{inity}$ and conformal algebras serve as dynamical symmetries in quantum Hall fluids, predicting universal finite-size effects in their excitation spectra.

Contribution

It highlights the role of advanced symmetry algebras in explaining the universal properties of quantum Hall systems and their finite-size scaling behaviors.

Findings

Infinite $W_{inity}$ and conformal algebras act as dynamical symmetries.

These symmetries predict universal finite-size effects.

The approach offers insights into the underlying symmetry principles of quantum Hall fluids.

Abstract

The exactness and universality observed in the quantum Hall effect suggests the existence of a symmetry principle underlying Laughlin's theory. We review the role played by the infinite $W_{\infty }$ and conformal algebras as dynamical symmetries of incompressible quantum fluids and show how they predict universal finite-size effects in the excitation spectrum.