Quantum Hall effect in bilayer systems and the noncommutative plane: A toy model approach

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 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 θ, and only if θ varies from layer to layer in the QH system.