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arXiv:cond-mat/9603156 · Nuclear Physics B

Modular invariance, self-duality and the phase transition between quantum Hall plateaus

Eduardo Fradkin, Steven Allan Kivelson

Published Sep 1, 1996• 79 citations
arXivHTMLPDF
DOI
10.1016/0550-3213(96)00310-0

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We investigate a model of interacting charged particles in two space dimensions, with manifest invariance under duality and periodicity under flux attachment. This model, introduced by Fradkin and Kivelson (1996 Nucl. Phys. B 474 543), shares many qualitative features of real quantum Hall systems. We extend this model to the case of finite filling fraction, i.e., to physical systems without particle–hole symmetry and without time-reversal invariance. We derive the transformation laws for the the average currents and prove that they have an SL (2, Z ) symmetry. We can then calculate the filling factors at the modular fixed points and further explore the topological order of the model by constructing the hierarchy of states.