  In this thesis we have used Quantum Monte Carlo techniques to study two
systems that can be regarded as the archetype for neutral strongly interacting
systems: 4He, and its fermionic counterpart 3He.More specifically, we have used
the Path Integral Ground State and the Path Integral Monte Carlo methods to
study a system of two dimensional 3He (2d-3He) and a system of 4He adsorbed on
Graphene-Fluoride (GF) and Graphane (GH) at both zero and finite temperature.
The purpose of the study of 4He on GF (GH) was the research of new physical
phenomena, whereas in the case of 2d-3He it was the application of novel
methodologies for the ab-initio study of static and dynamic properties of Fermi
systems. In the case of 2d-3He we have computed the spin susceptibility as
function of density which turned out to be in very good agreement with
experimental data; we have also obtained the first ab-initio evaluation of the
zero-sound mode and the dynamic structure factor of 2d-3He that is in
remarkably good agreement with experiments. In the case of 4He adsorbed on GF
(GH), we determined the zero temperature equilibrium density of the first
monolayer of 4He showing also that the commensurate sqrt(3) x sqrt(3) R30 phase
is unstable on both substrates; at equilibrium density we found that 4He on GF
(GH) is a modulated superfluid with an anisotropic phono-rotonic spectrum; at
high coverages we found an incommensurate triangular solid and, on both GF and
GH, a commensurate phase at filling factor x= 2/7 that is locally stable or at
least metastable. Remarkably, in this commensurate solid phase and for both GF
and GH, our computations show preliminary evidence of the presence of a
superfluid fraction.
