My PhD thesis - Condensed Matter Theory - Imperial College London

Chapter 7
The electronic ground-state wave
function from classical plasmon
normal modes
A prerequisite for a successful quantum Monte Carlo simulation is a trial wave
function of good quality. Conventionally, the many-electron trial wave function
takes the form
Ψ T (X) = e J(X) D ↑ (R ↑ )D ↓ (R ↓ ) (7.1)
where D ↑ and D ↓ are up- and down-spin determinants made up of density-functional
or Hartree-Fock single-electron orbitals. The quality of these orbitals sets a hard
limit on the accuracy of the QMC simulation in variational or fixed-node diffusion
Monte Carlo. The Jastrow factor, J, cannot alter the position of the nodes, and
therefore cannot improve the fixed-node DMC energy; however, a good Jastrow factor
significantly improves both the ground-state energy in VMC and the efficiency
of fixed-node DMC simulations. In certain circumstances, a poor-quality Jastrow
factor can make DMC simulations impossible, because the consequent population
fluctuations become unmanageable. This is the case for the jellium slab system,
which also suffers from the problem that optimising the Jastrow factor is very difficult;
in systems such as this, it is very important to obtain as much information as
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