Scaling theory of the fractional quantum Hall effect

Abstract

A new class of variational wave functions is proposed for the fractional quantum Hall effect in the presence of disorder at arbitrary electron densities. A consequence of these wave functions is a law of corresponding states which relates the behavior of the system in the fractional Hall regime to that in the integer Hall regime. For example, it is shown that the transition from the 1/3 to 2/5 plateau should be characterized by the same critical exponents as the transition between integer plateaus, while the transition between the 1 and 4/3 plateaus may be first order, and thus have no critical behavior.