My PhD thesis - Condensed Matter Theory - Imperial College London

Chapter 10
Conclusions
The original motivation for the work contained in this thesis was to resolve the
controversy over the surface energy of jellium; the calculations contained in the
final chapter suggest that this goal is close to being achieved. If the VMC results
reported here are supported by DMC simulations, the extended-system QMC results
will have been brought into line with those obtained using all other methods. This
is a vital step if one is to have confidence in future QMC simulations of extended
surface systems.
In working towards this goal, several techniques have been developed and investigated
which may have applications in different areas. First of all, the MPC
interaction has been introduced as a substitute for the Ewald interaction in quasi-
2D simulations. Although it does not reduce the Coulomb finite-size errors in such
systems, it is significantly faster than the Ewald interaction, and is therefore recommended
for future work on slabs.
An explanation of the Coulomb finite-size error, and its resistance to the MPC,
has also been provided. The model developed here leads to an error with the correct
sign; the next step is to estimate the scaling of the finite-size error with system
size, based on this model. An important lesson from this work is that the Coulomb
finite-size errors in quasi-2D systems can be large, even for large cells, and need to
be dealt with carefully.
A large part of this thesis is devoted to the connection between plasmons and
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