Quantum Monte Carlo studies of soft Bosonic systems and Minimum Energy Pathways.

In this thesis, we make use of Monte Carlo techniques to address two rather different subjects in condensed matter physics. The first study deals with the characterization of a relatively novel and elusive phase of matter, the so-called supersolid, in which crystalline order and dissipationless flow coexist. While supersolidity is a well studied phenomenology in lattice models, we will be working here in continuous space, where much fewer results are available. Specifically, we study a soft core Bosonic system, quantum analog of thoroughly studied classical models, which displays an unambiguous supersolid phenomenology. In this system such a behavior is not obtained through Bose Condensation of lattice defects, but rather it is mean field in character. By computer simulations we characterize many properties of the system: of these, the most prominent are the phase diagram of the system and its excitation spectrum. This study is loosely related to the ultracold atom experimental field, as it is speculated that interparticle potential pertaining to the same class of the one employed here may be realized in this context. After the recent (and apparently definitive) ruling out of supersolidity effects in ^4He, it seems fair to state that ultracold atoms are the most promising candidate for the observation of this phenomenology. In this section we employ our own implementation of the worm algorithm on the continuum. The second part of this thesis is instead related to electronic structure, more specifically to the study of minimum energy pathways of reactions calculated via quantum Monte Carlo methods. In particular, we aim at assessing the computational feasibility and the accuracy of determining the most significant geometries of a reaction (initial/final and transition state) and its energy barrier via these stochastic techniques. To this end, we perform calculations on a set of simple reactions and compare the results with density functional theory and high level quantum chemistry calculations. We show that the employed technique indeed performs better than density functional for both geometries and energy barrier. Therefore our methodology is a good candidate to study reactions in which an high accuracy is needed, but it is not possible to employ high level quantum chemistry methods due to computational limitations. We believe that this study is significant also because of its systematic use of forces from Monte Carlo simulations. Although several studies have addressed various aspects of the problem of computing forces within quantum Monte Carlo accurately and efficiently, there is little awareness that such estimators are in fact mature, and consequently there are very few studies which actually employ them. We hope to show here that these estimators are actually ready to be used and provide good results. In this section we have mainly developed interfaces for existing Quantum Monte Carlo codes.