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，分数量子厅效应（FQHE）会发挥主机的理论上有趣的行为，例如形成不可压缩的液态状态 - 造成霍尔电导率的量化 - 以及具有分数电荷和分数电荷的准颗粒激发统计数据。 FQHE是一种根本非扰动效应，其中物理学受强电子 - 电子相互作用的控制。尽管诸如Laughlin的变异波函数，复合费米片图片和Chern-Simons仪表理论之类的方法已经获得了深刻的定性见解，但该问题仍然远未被完全理解。这部分是因为该问题的高度相关性质已经阻止了大量电子的任何准确的数值计算。该项目的目的是使用多体绿色的功能形式主义和图表蒙特卡洛进行此类计算。