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The search for spontaneous pattern formation in equilibrium phases withgenuine quantum properties is a leading direction of current research. In thiswork we investigate the effect of quantum fluctuations - zero point motion andexchange interactions - on the phases of an ensemble of bosonic particles withisotropic hard-soft corona interactions. We perform extensive path-integralMonte Carlo simulations to determine their ground state properties. A richphase diagram, parametrized by the density of particles and the interactionstrength of the soft-corona potential, reveals supersolid stripes, kagome andtriangular crystals in the low-density regime. In the high-density limit weobserve patterns with 12-fold rotational symmetry compatible with periodicapproximants of quasicrystalline phases. We characterize these quantum phasesby computing the superfluid density and the bond-orientational order parameter.Finally, we highlight the qualitative and quantitative differences of ourfindings with the classical equilibrium phases for the same parameter regimes.

Superstripes and quasicrystals in bosonic systems with hard-soft corona interactions