The mean-field Bose glass in quasicrystalline systems

Abstract

We confirm the presence of a mean-field Bose glass (BG) 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-André (AA) 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 BG 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 AA 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 BG in certain regimes. This results in a lobe-like structure for the mean-field BG in the 2D AA 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 BG phase is present, as expected for

Phase Properties of Interacting Bosons in Presence of Quasiperiodic and Random Disorder

“…All these phase diagrams are in qualitative agreement with the QMC [61] and MFA results obtained in Ref. [62,63], where the signature of the QM phase, namely, the wSF or the weak BG (wBG) is also observed, and the wSF phase seems to stabilize at larger values of λ/U . For ∆/U = 0.2, the disorder introduces the BG phase, and due to localization effects, the chemical potential is shifted up or down by an amount ±∆/2 around the MI lobe [Fig.…”

“…For the random disorder, we choose a uniformly distributed energies, ǫ i from a box distribution [-∆, ∆], where ∆ denotes the strength of the random on-site potential [51,60]. For the other choice, ǫ i represents the two dimensional QP disorder at a site in a 2D square lattice, i ∈ (n, m) which is given by, [61][62][63]66]…”

“…Although a large number of studies so far have focussed on the effect of random disorder present in the BHM, unfortunately it remains highly unexplored how a quasiperiodic potential will influence the quantum phases of interacting bosons in optical lattices. Very recently, the ground state phase diagram of a twodimensional ultracold Bose gas in optical lattices in presence of QP disorder has been studied using QMC [61] and MFA [62,63] techniques. In addition to the BG phase, they have found signatures of an additional phase, namely, the quasiperiodic induced mixed (QM) phase along with the BG phase.…”

Hubbard Models for Quasicrystalline Potentials

“…Quantum Monte-Carlo [48]) that will be facilitated by the Hubbard model developed in this work. One might, in analogy to other disordered or quasiperiodic lattices, expect it to contain superfluid and Mottinsulating phases that are separated by the compressible Bose-glass phase [45,[48][49][50][51][52][53][54][55][56][57][58][59]. While the existence of Mott-insulating phases is a priori not clear, we can already draw some conclusions from the developed Hubbard model:…”

Finite-temperature phases of trapped bosons in a two-dimensional quasiperiodic potential

“…Recently, a number of studies have investigated the properties of interacting bosons in two-dimensional quasicrystalline potentials on quasicrystalline lattices in continuous space [19], in the tight-binding limit [20], and on a square lattice through the 2D Aubry-André model [21,22]. Some of these works have delineated phase diagrams in the mean-field approximation, and for strongly interacting particles; they have shown that regions of BG appear between the superfluid (SF) and Mott insulator (MI) phases, similarly to the disordered case.…”