Dolan, Brian P. (1999) Duality and the modular group in the quantum Hall effect. Journal of Physics A: Mathematical and General, 32 (21). L243-L248. ISSN 0305-4470

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Abstract

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 |p1q2-p2q1| = 1 for transitions between quantum Hall states characterized by filling factors nu1 = p1/q1 and nu2 = p2/q2; 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.

Item Type:	Article
Keywords:	Duality; modular group; quantum Hall effect; complex conductivity;
Academic Unit:	Faculty of Science and Engineering > Mathematical Physics
Item ID:	10486
Identification Number:	https://doi.org/10.1088/0305-4470/32/21/101
Depositing User:	Dr. Brian Dolan
Date Deposited:	14 Feb 2019 16:49
Journal or Publication Title:	Journal of Physics A: Mathematical and General
Publisher:	Institute of Physics
Refereed:	Yes
URI:	https://iopscience.iop.org

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