  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.
