My PhD thesis - Condensed Matter Theory - Imperial College London

CHAPTER 8. APPLYING THE PLASMON NORMAL MODE THEORY TO
SLAB SYSTEMS
1
0.8
L c
= 5.0
L c
= 10.0
L c
= 15.0
L c
= 20.0
0.6
χ − χ bulk
0.4
0.2
0
0 s
z
Figure 8.13: The one-body term χ cusp , for various values of the cut-off distance L c , calculated
using equation (8.119); this equation was derived using the approximation of constant electron
density within the slab. This term is designed to combat the density-changing effects of u cusp . As
L c becomes large, the curves tend to a limit, because the decay of u cusp is then dominated by k c
rather than L c .
inappropriate ones) is
[
Ψ = exp − 1 ∑(
)
u cusp (x i , x j ) + u s
2
pl(r i , r j )
i≠j
+ ∑ (
χ s bulk(r i ) + χ cusp (r i ) − 1 2 us pl(r i , r i )) ] D ↑ (R ↑ )D ↓ (R ↓ ).
i
(8.121)
8.4 Results
In order to test the plasmon-derived Jastrow factor, variational Monte Carlo simulations
were carried out for the two versions of the jellium slab system described
in chapter 5. For both systems, a cell containing 600 electrons was used, with the
154