We discuss the emergence of novel quantum phases in simple bosonic extended Hubbard models where particles interact via soft-shoulder potentials. In one dimension, we demonstrate that the low energy phase can be a conformal cluster Luttinger liquid where the microscopic degrees of freedom correspond to mesoscopic ensembles of particles . This phase has qualitatively new features with respect to the conventional Tomonaga-Luttinger liquid . In two dimensions, we provide a microscopic path for the realization of an exotic superglass phase, where superfluidity coexists with structural disorder. Remarkably, such a phase occurs in the absence of any externally imposed frustration, e.g., in the lattice geometry or in the interactions . Given the simplicity and generality of the models, these phases may be relevant for experiments with Rydberg-dressed atoms confined to optical lattices.
 Cluster Luttinger Liquids of Rydberg dressed atoms in optical lattices, M. Mattioli, M. Dalmonte, W. Lechner, and G. Pupillo, Phys. Rev. Lett. 111, 165302 (2013)
 Cluster Luttinger liquids and emergent supersymmetric conformal critical points in the one-dimensional soft-shoulder Hubbard model, M. Dalmonte, W. Lechner, Z. Cai, M. Mattioli, A. M. Lauchli, and G. Pupillo, arXiv:1502.00396
 Superglass phase of Rydberg atoms, A. Angelone, F. Mezzacapo, and G. Pupillo, arXiv:1504.00346