My PhD thesis - Condensed Matter Theory - Imperial College London

CHAPTER 10.
CONCLUSIONS
the electronic ground-state wave function. A new approach to this connection has
been presented, based on physically intuitive ideas. The resulting prescription for
the long-wavelength correlations in the wave function agrees with previous work; the
value of the formalism presented here is that it is now much easier to incorporate
prior knowledge about plasmon normal modes in any given system.
This idea has been tested on the jellium slab system, with some success: the
plasmon-predicted Jastrow factor reduces the energy in VMC. However, the strong
long-wavelength correlations disrupt the electron density significantly, and although
the predicted one-electron term almost restores the original (and presumably correct)
density, this restoration is not perfect. In contrast, the short-ranged correlation
term developed here has a much weaker effect on the density, and the corresponding
analytic one-electron term is able to restore the original density almost exactly. One
important conclusion is that it appears to be more important to have the correct
density than to include all the long-wavelength correlations, and this makes the
short-ranged Jastrow factor more attractive.
Presumably, the best Jastrow factor would use both long- and short-ranged correlations,
and take the predicted one-electron term as a starting point; adding some
variational freedom to this term would then allow the correct density to be restored
while maintaining all the correlations. However, the aim here was to minimise the
need for optimisation, since this procedure is awkward for the jellium slab; therefore
only the short-ranged correlation term (and the corresponding density-restoring
function) were used in the calculations of the final chapter.
The density-restoring term corresponding to the short-ranged correlation function
was derived analytically, using a relationship which has been postulated by
other authors and which is automatically satisfied by the plasmon Jastrow factor.
This suggests that the relationship may hold generally in inhomogeneous systems,
and can provide a way to make the optimisation process much more efficient: a
starting-point for the one-electron term is provided analytically, depending on the
two-body term.
Two other techniques were shown to have little impact: alternative k-point sam-
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