The group $\Gamma (2)$ and the fractional quantum hall effect

Abstract

We analyze the action of the inhomogeneous modular group $\Gamma (2)$ on the three cusps of its principal fundamental domain in the Poincare half plane. From this, we obtain an exhaustive classification of the fractional quantum Hall numbers. This classification is somehow similar to the one given by Jain. We also present some resulting remarks concerning direct phase transitions between the different quantum Hall states.

11 pages Tex, 2 figures from request

References in corpus (2)

• The Non-Commutative Geometry of the Quantum Hall Effect
• Fusion & Tensoring of Conformal Field Theory and Composite Fermion Picture of Fractional Quantum Hall Effect

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