Derivation of the semicircle law from the law of corresponding states

We show that, for the transition between any two quantum Hall states, the semicircle law and the existence of a duality symmetry follow solely from the consistency of the law of corresponding states with the two-dimensional scaling flow. This puts these two effects on a sound theoretical footing, implying that both should hold exactly at zero temperature, independently of the details of the microscopic electron dynamics. This derivation also …