The integer quantum Hall plateau transition is a current algebra after all

Abstract

The scaling behavior near the transition between plateaus of the Integer Quantum Hall Effect (IQHE) has traditionally been interpreted on the basis of a two-parameter renormalization group (RG) flow conjectured from Pruisken's non-linear sigma model. Yet, the conformal field theory (CFT) describing the critical point remained elusive, and only fragments of a quantitative analytical understanding existed up to now. In the present paper we carry out a detailed analysis of the current-current correlation function for the conductivity tensor, initially in the Chalker-Coddington network model for the IQHE plateau transition and then in its exact reformulation as a supersymmetric vertex model. We develop a heuristic argument for the continuum limit of the non-local conductivity response function at criticality and thus identify a non-Abelian current algebra at level n = 4. Based on precise lattice expressions for the CFT primary fields we predict the multifractal scaling exponents of critical wavefunctions to be q(1-q)/4. The Lagrangian of the RG fixed-point theory for r retarded and r advanced replicas is proposed to be the GL(r|r)_4 Wess-Zumino-Witten model deformed by a truly marginal perturbation. The latter emerges from the non-linear sigma model by a natural scenario of spontaneous symmetry breaking.

v1: 40 pages, 4 figures; v2: 50 pages (four new sections: 4.3, 4.4, 4.12, 4.13); v3: 60 pages (added section on spontaneously broken symmetry), published version

References in corpus (4)

• Anderson Transitions
• Critical exponent for the quantum Hall transition
• Evidence for the PSL(2$|$2) Wess-Zumino-Novikov-Witten model as a model for the plateau transition in Quantum Hall effect: Evaluation of numerical simulations
• Gaussian free fields at the integer quantum Hall plateau transition

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