Investigating the fractional quantum Hall effect using diagrammatic techniques.

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.