Conclusive experimental evidence of a supersolid phase in any known condensed matter system is presently lacking. On the other hand, a supersolid phase has been recently predicted for a system of spinless bosons in continuous space, interacting via a broad class of soft-core, repulsive potentials. Such an interaction can be engineered in assemblies of ultracold atoms, providing a well-defined pathway to the unambiguous observation of this fascinating phase of matter. In this article, we study by first principle computer simulations the elementary excitation spectrum of the supersolid, and show that it features two distinct modes, namely a solid-like phonon and a softer collective excitation, related to broken translation and gauge symmetry respectively.

The low temperature phase diagram of Bose soft disks in two dimensions is studied by numerical simulations. It is shown that a supersolid cluster phase exists, within a range of the model parameters, analogous to that recently observed for a system of aligned dipoles interacting via a softened potential at short distance. These findings indicate that a long-range tail of the interaction is unneeded to obtain such a phase, and that the soft-core repulsive interaction is the minimal model for supersolidity

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