The search for spontaneous pattern formation in equilibrium phases with genuine quantum properties is a leading direction of current research. We investigate the effect of quantum fluctuations - zero-point motion and exchange interactions - on the phases of an ensemble of bosonic particles with local and nonlocal interactions to determine their ground state properties. In the high-density limit, we observe patterns with 12-fold rotational symmetry compatible with periodic approximants of quasicrystalline phases and their connection to related phases in soft-matter physics. In the second part, I present results for a system of 2D trapped bosons in a quasiperiodic potential at finite temperature. Alongside the superfluid, normal fluid, and insulating phases, we demonstrate the existence of a Bose glass phase, which is robust to thermal fluctuations for a set of parameters within current experiments with quasi-2D optical confinement.
 B. Abreu, F. Cinti, and T. Macrì, Phys. Rev. B 105, 094505 (2022)
 M. Ciardi, T. Macrì, and F. Cinti, Phys. Rev. A 105, L011301 (2022)
 A. Mendoza-Coto, R. Turcati, V. Zampronio, R. Díaz-Méndez, T. Macrì, F. Cinti, Phys. Rev. B 105, 134521 (2022)
 N. Defenu, T. Donner, T. Macrì, G. Pagano, S. Ruffo, A. Trombettoni, arXiv:2109.01063 (2021)