The Jastrow trial-wavefunction obtained in
the previous section givers a very good approximation for the ground
state wavefunction of dilute Bose gases.
One can appreciate this by comparing the VMC and
DMC energies (Fig. 3.1).
On this plot the relative error of the energy
estimate is presented as a function of the density.
The coincidence of DMC and VMC results is very good
in the density region and remains quite good
for higher densities.
Figure 3.1:
Energy comparison between VMC and DMC calculations
at different densities
The energy obtained in VMC is always larger than the ground state
energy (see Fig. 3.1). In other words, variational
simulations always give an upper bound to the ground state
energy.