Superuniversality of Quantum Hall Interplateaux Transitions and SL(2,Z) Modular Transformations

The theoretical understanding of “superuniversality,” [1] the phenomenon where all quantum Hall (QH) plateaux transitions exhibit the same correlation length and dynamical critical exponents, is a long-standing challenge. Although the correspondence rule of Ref. [2] says that superuniversality should arise at critical points between plateaux related by the addition of Landau levels, a particle-hole transformation, or flux attachment, it is not clear how such insensitivity would be realized theoretically. Here we introduce a new effective description with an emergent U(N) gauge symmetry for a transition between an integer QH state and an insulator. We then use SL(2,Z) transformations, which formally implement the transformations in Ref. [2], to generate descriptions for a large class of QH transitions. In the t' Hooft large N limit, the correlation length and dynamical critical exponents are the same at all such transitions in the absence of disorder. We argue that this conclusion survives away from the large N limit using recent duality conjectures, thereby providing theoretical support for the observed superuniversality.

[1] RMP 69, 315 (1997).
[2] PRB 46, 2223 (1992).