Quantum Hall fluids, Laughlin wave functions, and ideals in the Weyl algebra

TL;DR

This paper explores the mathematical connections between quantum Hall fluids, Laughlin wave functions, and algebraic structures like the Weyl algebra, revealing new insights into their group-theoretic and ideal-theoretic descriptions.

Contribution

It establishes a novel link between non-commutative fluid models, Calogero--Moser systems, and ideals in the Weyl algebra, advancing the theoretical understanding of quantum Hall effects.

Findings

Calogero--Moser systems model fractional quantum Hall fluids.

Laughlin wave functions arise from Lie algebra reductions.

Right ideals of the Weyl algebra correspond to fluid sources.

Abstract

It is known that non-commutative fluids used to model the Fractional Quantum Hall effect give Calogero--Moser systems. The group-theoretic description of these as reductions of free motion on type A Lie algebras leads directly to Laughlin wave functions. The Calogero--Moser models also parametrise the right ideals of the Weyl algebra, which can be regarded as labelling sources in the fluid.