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

低维量子系统在所谓的量子临界点上表现出令人惊讶的特性，因为这些临界点通常是由量子涨落以一种非直观的方式驱动的。这种量子临界行为的一个最突出的例子是量子霍尔效应中的平台转变，该转变源于电子在具有无序势的两个空间维度中的定域态和离域态的相互作用。这种效应包括所有电子输运性质的精确量子化，并导致例如作为磁场函数的霍尔电阻率中的平台的发展。对无序二维粒子系统的理论理解是基于到具有超对称性的一维相互作用量子自旋链的映射，或者基于到Chalker-Coddington类型的超对称二维网络模型的映射。这一方案的研究项目旨在利用可积系统领域的现代技术对这些模型进行推导和研究。特别是，Chalker-Coddington网络模型的精确可解情况应该被识别和调查。其目的是分析计算这些系统的临界性质，即临界指数和相关函数的渐近性。

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.