Zirnbauer, Martin R. (2019). The integer quantum Hall plateau transition is a current algebra after all. Nucl. Phys. B, 941. S. 458 - 507. AMSTERDAM: ELSEVIER SCIENCE BV. ISSN 1873-1562
Full text not available from this repository.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 (NL sigma M). 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 Delta(q) = q(1 - q)/4. The Lagrangian of the RG-fixed point theory for rretarded and radvanced replicas is proposed to be the GL(r vertical bar r)(n= 4) Wess-Zumino-Witten model deformed by a truly marginal perturbation. The latter emerges from the NLsM by a natural scenario of spontaneous symmetry breaking. (C) 2019 The Author. Published by Elsevier B.V.
| Item Type: | Journal Article | ||||||||
| Creators: |
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| URN: | urn:nbn:de:hbz:38-152537 | ||||||||
| DOI: | 10.1016/j.nuclphysb.2019.02.017 | ||||||||
| Journal or Publication Title: | Nucl. Phys. B | ||||||||
| Volume: | 941 | ||||||||
| Page Range: | S. 458 - 507 | ||||||||
| Date: | 2019 | ||||||||
| Publisher: | ELSEVIER SCIENCE BV | ||||||||
| Place of Publication: | AMSTERDAM | ||||||||
| ISSN: | 1873-1562 | ||||||||
| Language: | English | ||||||||
| Faculty: | Faculty of Mathematics and Natural Sciences | ||||||||
| Divisions: | Faculty of Mathematics and Natural Sciences > Department of Physics > Institute for Theoretical Physics | ||||||||
| Subjects: | Mathematics Physics |
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| Refereed: | Yes | ||||||||
| URI: | http://kups.ub.uni-koeln.de/id/eprint/15253 |
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