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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.
Entanglement of spatial bipartitions, used to explore lattice models in condensed matter physics, may be insufficient to fully describe itinerant quantum many-body systems in the continuum. We introduce a procedure to measure the Renyi entanglement e
We study a harmonically confined Bose-Bose mixture using quantum Monte Carlo methods. Our results for the density profiles are systematically compared with mean-field predictions derived through the Gross-Pitaevskii equation in the same conditions. T
We study the fluctuation properties of a one-dimensional many-body quantum system composed of interacting bosons, and investigate the regimes where quantum noise or, respectively, thermal excitations are dominant. For the latter we develop a semiclas
We study a resonant Bose-Fermi mixture at zero temperature by using the fixed-node diffusion Monte Carlo method. We explore the system from weak to strong boson-fermion interaction, for different concentrations of the bosons relative to the fermion c
In this thesis, I go through the well-known solutions to the one and two-particle systems trapped in a quantum harmonic oscillator and then continue to the three, four and many-body quantum systems. This is done by developing new analytical models an