Quantum Hall Effect In Bilayer Systems And The Noncommutative Plane: A Toy Model Approach

TL;DR

This paper introduces a toy model for Coulomb interactions in bilayer Quantum Hall systems, exploring modifications in the noncommutative plane and highlighting the effects of varying noncommutativity parameters across layers.

Contribution

It presents a perturbative toy model that simulates Coulomb interactions in bilayer Quantum Hall systems within a noncommutative geometric framework.

Findings

Coulomb interaction is modified at higher order in the noncommutativity parameter.

Variation of the noncommutativity parameter between layers affects Coulomb interactions.

The model provides insights into the interplay between noncommutativity and bilayer Quantum Hall physics.

Abstract

We have presented a quantum mechanical toy model for the study of Coulomb interactions in Quantum Hall (QH) system. Inclusion of Coulomb interaction is essential for the study of {\it{bilayer}} QH system and our model can simulate it, in the compound state, in a perturbative framework. We also show that in the noncommutative plane, the Coulomb interaction is modified at a higher order in the noncommutativity parameter $\theta$, and only if $\theta$ varies from layer to layer in the QH system.