| Besides describing the Quantum Monte Carlo (QMC) methodology, this thesis consists of three main aspects. To begin with, we explore two strongly correlated systems: supersolids and the 2D Coulomb phase diagram. We use QMC methods, especially path integral Monte Carlo, to approach these problems. We also devise algorithms that help alleviate, in certain situations, the dominant asymptotic computational bottleneck to QMC simulations: the O( n3) scaling for calculating determinant ratios.;With respect to supersolids, we give strong numerical evidence that the perfect commensurate lattice of solid 4He does not form a BEC. Additionally, we calculate the effective mass of vacancies in solid 4He as well as their interparticle attraction and argue that these values preclude a vacancy induced mechanism for supersolids. Finally, we explore metastable high pressure liquid 4He. We calculate the extension of superfluidity into the metastable region of the phase diagram finding there are regions where it sustains superfluidity. We also calculate the equation of state, and the value of the roton gap as a function of pressure.;We map out the 2D Coulomb distinguishable particle phase diagram. We show the existence of an exceptionally large re-entrant liquid phase. We argue that the hexatic phase in this system differs from canonical KT theory for a variety of reasons including the fact that the critical exponent for the hexatic phase extends over a much wider range than in short-range systems. We find metastable mesoscopic phases, but argue that these mesoscopic phases would have to be larger then the size of the universe for them to exist in equilibrium.;Finally, we explore three algorithms for speeding up the calculation of determinant ratios specifically for insulators. These algorithms take advantage both of the locality of physics and the sparsity of the matrices that are used in the quantum wave functions that represent these insulators. |
