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

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.

Slightly expanded version, Eqs. (18) and (19) added, Conclusions unchanged, To appear in Phys.Lett.A

References in corpus (9)

• String Theory and Noncommutative Geometry
• Noncommutative Field Theory
• Fractional Quantum Hall Effect of Composite Fermions
• Hall Effect in Noncommutative Coordinates
• Energy Crisis or a New Soliton in the Noncommutative CP(1) Model?
• Bosonization in the Noncommutative Plane
• Ground-State Structure in $\nu =2$ Bilayer Quantum Hall Systems
• Novel Families of Fractional Quantum Hall States : A Berry Phase Approach
• Electrons-Holes on Noncommutative Plane and Hall Effect

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