| In this dissertation I present results for lattice boson systems based on quantum Monte Carlo simulations by the Worm algorithm. Lattice bosons can be realized by ultracold gases in optical lattices and, under certain conditions, they are described by the Bose-Hubbard model. I will discuss the ground state, i.e. the phase diagram and properties of elementary excitations, as well as finite temperature thermodynamic properties of the two- and three-dimensional systems. These results provide bench-marks and guidance for experimentalists. I will also discuss the phase diagram of the one-dimensional hard-core Bose-Hubbard model with three-body interactions. The model is realized by cold polar molecules in optical lattices. The ground state presents a novel solid phase at unconventional filling, characterized by coexisting charge density wave and bond orders. Such phase has not been predicted by the preexisting mean field theory. |
