The Mean-Field Bose Glass in Quasicrystalline Systems

Abstract

We confirm the presence of a mean-field Bose glass in 2D quasicrystalline Bose-Hubbard models. We focus on two models where the aperiodic component is present in different parts of the problem. First, we consider a 2D generalisation of the Aubry-Andr\'e model, where the lattice geometry is that of a square with a quasiperiodic onsite potential. Second, we consider the randomly disordered vertex model, which takes aperiodic tilings with non-crystalline rotational symmetries, and forms lattices from the vertices and lengths of the tiles. For the disordered vertex models, the mean-field Bose glass forms across large ranges of the chemical potential, and we observe no significant differences from the case of a square lattice with uniform random disorder. Small variations in the critical points in the presence of random disorder between quasicrystalline and crystalline lattice geometries can be accounted for by the varying coordination number and the different rotational symmetries present. In the 2D Aubry-Andr\'e model, substantial differences are observed from the usual phase diagrams of crystalline disordered systems. We show that weak modulation lines can be predicted from the underlying potential and may stabilise or suppress the mean-field Bose glass in certain regimes. This results in a lobe-like structure for the mean-field Bose glass in the 2D Aubry-Andr\'e model, which is significantly different from the case of random disorder. Together, the two quasicrystalline models studied in this work show that the mean-field Bose glass phase is present, as expected for 2D quasiperiodic models. However, a quasicrystalline geometry is not sufficient to result in differences from crystalline realisations of the Bose glass, whereas a quasiperiodic form of disorder can result in different physics, as we observe in the 2D Aubry-Andr\'e model.