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

量子霍尔效应中平台跃迁的 Chalker-Coddington 网络模型中的可积结构

• 批准号: 188611238
• 负责人: Professor Dr. Andreas Kluemper
• 金额: --
• 依托单位: Fachgruppe Physik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2011
• 资助国家: 德国
• 起止时间: 2010-12-31 至 2013-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/188611238?language=en
• 关键词: Integrable; structures; Chalker; Coddington; network

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.

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，因为这些量子通常是由量子波动驱动的，通常以不直觉的方式驱动。这种量子临界行为的最突出的例子是量子厅效应的高原转变，源自两个具有无序潜力的空间维度的电子的局部和离域状态。该效应包括所有电子传输特性的精确量化，例如导致磁场电场中高原的发展。对具有无序的二维粒子系统的理论理解是基于对具有超对称性的一维相互作用量子旋转链的映射，或者与Chalker-Coddington Type的超对比的二维网络模型。该提案的研究项目旨在通过使用来自可集成系统领域的现代技术来衍生和研究此类模型。特别是，应确定和研究Chalker-Coddington网络模型的确切可解决的案例。目的是对这些系统的关键特性的分析计算，即关键指数和相关函数的渐近学。