A key ingredient of the DMC algorithm is the branching process
(3.29). The algorithm is exact, i.e. gives the exact
ground-state energy of the system, in the limit of an infinite
population of walkers. However it is necessary to understand how
many walkers have to be used in practice to estimate the energy
with a given value of accuracy [27].
In Fig. 3.2 we plot the energy for a given value of the
density
as a function of the mean number of
walkers. In all simulations carried out in this work we have used
about one hundred walkers.
Figure 3.2:
Hard-spheres at
. Dependence of
the energy on the size of the population of walkers.