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We study the low-temperature phases of interacting bosons on atwo-dimensional quasicrystalline lattice. By means of numerically exact PathIntegral Monte Carlo simulations, we show that for sufficiently weakinteractions the system is a homogeneous Bose-Einstein condensate, whichdevelops density modulations for increasing filling factor. The simultaneousoccurrence of sizeable condensate fraction and density modulation can beinterpreted as the analogous, in a quasicrystalline lattice, of supersolidphases occurring in conventional periodic lattices. For sufficiently largeinteraction strength and particle density, global condensation is lost andquantum exchanges are restricted to specific spatial regions. The emergingquantum phase is therefore a Bose Glass, which here is stabilized in theabsence of any source of disorder or quasidisorder, purely as a result of theinterplay between quantum effects, particle interactions and quasicrystallinesubstrate. This finding clearly indicates that (quasi)disorder is not essentialto observe Bose Glass physics. Our results are of interest for ongoingexperiments on (quasi)disorder-free quasicrystalline lattices.

Quasicrystalline Bose glass in the absence of disorder and quasidisorder