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

Details The group $Γ(2)$ and the fractional quantum hall effect The group $Γ(2)$ and the fractional quantum hall effect

1996-05-06

arxiv.org/abs/cond-mat/9605030v1

Physics

Condensed Matter

11 pages Tex, 2 figures from request

Scientific paper

10.1016/S0375-9601(96)00830-4

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.

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