Network of Edge States: A Random Josephson Junction Array Description

We construct a generalization of the Chalker-Coddington network model to the case of the fractional quantum Hall effect, which describes the tunneling between multiple chiral edges. We derive exact local and global duality symmetries of this model, and show that its infrared properties are identical to those of a disordered planar Josephson junction array in a weak magnetic field, which implies that they are in the same universality class. The zero frequency Hall resistance of the system, which was expressed through exact correlators of the tunneling fields, is shown to be quantized both in the quantum Hall limit and in the limit of the perfect Hall insulator.