Two-dimensional and novel quasi-two-dimensional quantum liquids

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