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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.
We exploit mappings between quantum and classical systems in order to obtain a class of two-dimensional classical systems with critical properties equivalent to those of the class of one-dimensional quantum systems discussed in a companion paper (J.
The existence of nonlinear objects of the vortex type in two-dimensional magnetic systems presents itself as one of the most promising candidates for the construction of nanodevices, useful for storing data, and for the construction of reading and wr
Restricted Boltzmann machines (RBM) and deep Boltzmann machines (DBM) are important models in machine learning, and recently found numerous applications in quantum many-body physics. We show that there are fundamental connections between them and ten
Grand canonical Monte Carlo simulations have been performed to determine the adsorption behavior of Ar and Kr atoms on the exterior surface of a rope (bundle) consisting of many carbon nanotubes. The computed adsorption isotherms reveal phase transit
Monte Carlo simulations and finite-size scaling analysis have been carried out to study the critical behavior in a two-dimensional system of particles with two bonding sites that, by decreasing temperature or increasing density, polymerize reversibly