In a recent study we have reported a new type of trial wave function
symmetric under the exchange of particles and which is able to describe a
supersolid phase. In this work, we use the diffusion Monte Carlo method and
this model wave function to study the properties of solid 4He in two- and quasi
two-dimensional geometries. In the purely two-dimensional case, we obtain
results for the total ground-state energy and freezing and melting densities
which are in good agreement with previous exact Monte Carlo calculations
performed with a slightly different interatomic potential model. We calculate
the value of the zero-temperature superfluid fraction \rho_{s} / \rho of 2D
solid 4He and find that it is negligible in all the considered cases, similarly
to what is obtained in the perfect (free of defects) three-dimensional crystal
using the same computational approach. Interestingly, by allowing the atoms to
move locally in the perpendicular direction to the plane where they are
confined to zero-point oscillations (quasi two-dimensional crystal) we observe
the emergence of a finite superfluid density that coexists with the periodicity
of the system.Comment: 16 pages, 8 figure