Investigating the fractional quantum Hall effect using diagrammatic techniques.

分数量子霍尔效应（FQHE）被认为是许多理论上有趣的行为的主，比如不可压缩液态的形成——这是霍尔电导率的量子化的原因——以及具有分数电荷和统计的准粒子激发。FQHE基本上是一种非微扰效应，其中的物理是由强电子-电子相互作用控制的。虽然从诸如劳克林的变分波函数、复合费米子图和陈恩-西蒙斯规范理论等方法中获得了深刻的定性见解，但这个问题仍然远远没有被完全理解。这在一定程度上是因为这个问题的高度相关性质迄今为止阻碍了对大量电子进行精确的数值计算。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。

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.