Investigating the fractional quantum Hall effect using diagrammatic techniques.

使用图表技术研究分数量子霍尔效应。

• 批准号: 2444312
• 金额: --
• 依托单位: King's College London
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2020
• 资助国家: 英国
• 起止时间: 2020 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2444312
• 关键词: Investigating; fractional; quantum; Hall; effect

The fractional quantum Hall effect (FQHE) is known to play host to a wealth of theoretically interesting behaviour such as the formation of incompressible liquid states - which is responsible for the quantisation of the Hall conductivity - and quasi-particle excitations which have fractional charge and statistics. The FQHE is a fundamentally non-perturbative effect, in which the physics is governed by the strong electron-electron interactions. While deep qualitative insight has been gained from methods such as Laughlin's variational wavefunction, the composite Fermion picture and Chern-Simons gauge theory, the problem still remains far from being completely understood. This is in part because the highly-correlated nature of the problem has thus far prevented any accurate numerical calculations for large numbers of electrons. The aim of this project is to perform such calculations using the many-body Green's function formalism and diagrammatic Monte Carlo.

众所周知，分数量子霍尔效应(FQHE)是许多理论上有趣行为的宿主，例如不可压缩液态的形成--这是霍尔电导率的量化--以及具有分数电荷和统计性质的准粒子激发。FQHE是一种基本的非微扰效应，其中物理受强电子-电子相互作用的支配。虽然Laughlin的变分波函数、复合费米子图和Chern-Simons规范理论等方法已经取得了深刻的定性见解，但这个问题仍然远未完全被理解。这在一定程度上是因为到目前为止，这个问题的高度关联性质阻碍了对大量电子的任何准确的数值计算。这个项目的目的是使用多体格林函数形式和图解蒙特卡罗来执行这样的计算。