Peer-Reviewed Journal Details
Mandatory Fields
Dolan B.
1999
May
Journal of Physics A: Mathematical and General
Duality and the modular group in the quantum Hall effect
Published
()
Optional Fields
32
21
L243
L248
We explore the consequences of introducing a complex conductivity into the quantum Hall effect. This leads naturally to an action of the modular group on the upper-half complex conductivity plane. Assuming that the action of a certain subgroup, compatible with the law of corresponding states, commutes with the renormalization group flow, we derive many properties of both the integer and fractional quantum Hall effects including: universality; the selection rule |p 1q 2 - p 1q 2| = 1 for transitions between quantum Hall states characterized by filling factors v 1 = p 1/q 1 and v 2 = p 2/q 2; critical values of the conductivity tensor; and Farey sequences of transitions. Extra assumptions about the form of the renormalization group flow lead to the semicircle rule for transitions between Hall plateaux.
0305-4470
10.1088/0305-4470/32/21/101
Grant Details