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Résumé |
The Chalker-Coddington (CC, 1988) model is a simple 2D disordered lattice model for the Integer
Quantum Hall Effect (IQHE), and its exact solution is still an open problem. Using the supersymmetric
path-integral formulation of the CC model, we propose a truncation procedure, leading
to a loop model with loop fugacity n=0. In the same loop model with general n,
we identify an integrable manifold by a mapping to the dilute Birman-Wenzl-Murakami
(BWM) algebra. Moreover, a discrete parafermion exists exactly on this manifold,
as it is the case for several other loop models. The correspondence with BWM allows us to
conjecture a conformal field theory description for specific values of n, not including n=0.
We discuss numerical results at n=0, suggesting that it does not belong to the IQHE
universality class. However, it constitutes an integrable case for the first step of another
truncation procedure of the CC model, studied by Marston, Kondev and Tsai.
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