Integrable structures in Chalker-Coddington network models for plateau transitions in the quantum Hall effect

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Low-dimensional quantum systems exhibit surprising properties at so-called quantum critical points as these are driven by quantum fluctuations often in an unintuitive manner. A most prominent example of such a quantum critical behaviour is the plateau transition in the quantum Hall effect originating from the interplay of localized and delocalized states of electrons in two spatial dimensions with disorder potential. This effect comprises the exact quantization of all electronic transport properties and leads for instance to the development of plateaux in the Hall resistivity as a function of the magnetic field. The theoretical understanding of two-dimensional particle systems with disorder is based on mappings to one-dimensional interacting quantum spin chains with super-symmetry or alternatively to super-symmetric two-dimensional network models of Chalker- Coddington type. The research project of this proposal aims at the derivation as well as investigation of such models by use of modern techniques from the field of integrable systems. In particular, exactly solvable cases of Chalker-Coddington network models shall be identified and investigated. The aim is the analytical computation of the critical properties of these systems, i.e. of the critical exponents and the asymptotics of the correlation functions.