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表现出令人惊讶的特性，因为它们通常以一种不直观的方式由量子涨落驱动。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跃迁，它起源于具有无序势的二维空间中电子的局域和非局域状态的相互作用。这种效应包括所有电子输运特性的精确量化，并导致霍尔电阻率作为磁场函数的平台的发展。二维无序粒子系统的理论认识是基于映射到一维超对称的相互作用量子自旋链或超对称的Chalker- Coddington型二维网络模型。本提案的研究项目旨在利用可积系统领域的现代技术推导和研究这些模型。尤其需要对Chalker-Coddington网络模型的精确可解情况进行识别和研究。目的是解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.