Multipole Expansion in the Quantum Hall Effect

TL;DR

This paper develops a systematic multipole expansion approach for low-energy excitations in quantum Hall states, revealing their extended nature and connecting to known effective actions and Hall viscosity.

Contribution

It introduces a novel multipole expansion framework based on W-infinity symmetry to analyze quantum Hall excitations, extending previous effective theories.

Findings

Reproduces Wen and Wen-Zee actions

Identifies excitations as extended objects with multipolar moments

Links low-energy excitations to higher-spin fields

Abstract

The effective action for low-energy excitations of Laughlin's states is obtained by systematic expansion in inverse powers of the magnetic field. It is based on the W-infinity symmetry of quantum incompressible fluids and the associated higher-spin fields. Besides reproducing the Wen and Wen-Zee actions and the Hall viscosity, this approach further indicates that the low-energy excitations are extended objects with dipolar and multipolar moments.