In this Thesis, we report a detailed study of the ground-state properties of a set of quantum few- and many-body systems in one and two dimensions with different types of interactions by using Quantum Monte Carlo methods. Nevertheless, the main focus of this work is the study of the ground-state properties of an ultracold Bose system with dipole-dipole interaction between the particles. We consider the cases where the bosons are confined to a bilayer and multilayer geometries, that consist of equally spaced two-dimensional layers. These layers can be experimentally realized by imposing tight confinement in one direction. We specifically address the study of new quantum phases, their properties, and transitions between them. One expects these systems to have a rich collection of few- and many-body phases because the dipole-dipole interaction is anisotropic and quasi long-range.
We calculate the ground-state properties of unpolarized two-dimensional attractive fermions in the range from few to many particles. Using first-principles lattice Monte Carlo methods, we determine the ground-state energy, Tan's contact, momentum distribution, and single-particle correlation function. We investigate those properties for systems of $N=4,8,\ensuremath{\cdots},40$ particles and for a wide range of attractive couplings. As the attractive coupling is increased, the thermodynamic limit is reached at progressively lower
N due to the dominance of the two-body sector. At large momenta
k, the momentum distribution displays the expected ${k}^{\ensuremath{-}4}$ behavior, but its onset shifts from $k\ensuremath{\simeq}1.8{k}_{F}^{}$ at weak coupling towards higher
k at strong coupling.