My PhD thesis - Condensed Matter Theory - Imperial College London

CHAPTER 4.
ERRORS IN QMC SIMULATIONS
w
s
simulation cell
Figure 4.3: The effective system when applying periodic boundary conditions to the simulation
cell. The shaded areas represent the positive background; the electron density is similar, though
with less sharply-defined edges.
The electronic wave functions decay exponentially outside the slab, and any interaction
between slabs is negligible.
However, in QMC calculations, this is no longer true. Rather than a smooth
charge density, there is now a collection of individual electrons. Using the 3D Ewald
interaction (which is equivalent to applying periodic boundary conditions in all three
dimensions) introduces Coulomb finite-size errors; these were described in section
4.1.2. The form of the errors is not quite the same as in bulk systems: it is closer
to that created when attempting to model a defect in an infinite system by using
periodic boundary conditions (and thus repeating the defect).
It is not strictly necessary to use the 3D Ewald interaction, or to apply periodic
boundary conditions in the direction perpendicular to the slab; the quasi-2D version
of the Ewald interaction will be discussed later.
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