My PhD thesis - Condensed Matter Theory - Imperial College London

Abstract
This thesis will address the problem of carrying out electronic structure calculations
on quasi-2D systems, focusing on the use of quantum Monte Carlo methods and
using the quasi-2D electron gas as a test system.
Two techniques aimed at improving the accuracy of these simulations will be
proposed and tested:
• the use of a modified periodic Coulomb interaction to reduce finite-size errors.
It will be shown that the modified interaction does not reduce the finite-size
errors; this failure will be analysed and explained. However, it is significantly
faster than the conventional interaction, and is therefore recommended.
• the application of classical plasmon theory to improve the quality of trial wave
functions. A new, intuitive approach to the connection between plasmons and
the electronic wave function based on physical arguments will be presented.
The predictions for the general form of the wave function in inhomogeneous
materials agree with previous results obtained by other methods. In addition,
the new approach makes clear the role of classical plasmon normal modes; an
analysis of these modes in the case of the quasi-2D electron gas leads directly
to an improved wave function for this system.
Finally, a new calculation of the surface energy of the electron gas will be presented.
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