Ground state and excitation properties of soft-core bosons

We study the physics of soft-core bosons at zero temperature in two dimensions for a class of potentials that could be realised in experiments with Rydberg dressed Bose-Einstein condensates. We analyze the ground state properties of the system in detail and provide a complete description of the excitation spectra in both superfluid, supersolid and crystalline phase for a wide range of interaction strengths and densities. In addition we describe a method to extract the transverse gapless excitation modes in the phases with broken translational symmetry within the framework of path integral Monte Carlo methods.