We study the low-temperature phases of interacting bosons on a two-dimensional quasicrystalline lattice. By means of numerically exact path integral Monte Carlo simulations, we show that for sufficiently weak interactions the system is a homogeneous Bose-Einstein condensate that develops density modulations for increasing filling factor. The simultaneous occurrence of sizeable condensate fraction and density modulation can be interpreted as the analogous, in a quasicrystalline lattice, of supersolid phases occurring in conventional periodic lattices. For sufficiently large interaction strength and particle density, global condensation is lost and quantum exchanges are restricted to specific spatial regions. The emerging quantum phase is therefore a Bose glass, which here is stabilized in the absence of any source of disorder or quasidisorder, purely as a result of the interplay between quantum effects, particle interactions and quasicrystalline substrate. This finding clearly indicates that (quasi)disorder is not essential to observe Bose glass physics. Our results are of interest for ongoing experiments on (quasi)disorder-free quasicrystalline lattices.
We study the low-temperature phases of interacting bosons on a two-dimensional quasicrystalline lattice. By means of numerically exact path integral Monte Carlo simulations, we show that for sufficiently weak interactions the system is a homogeneous Bose-Einstein condensate that develops density modulations for increasing filling factor. The simultaneous occurrence of sizeable condensate fraction and density modulation can be interpreted as the analogous, in a quasicrystalline lattice, of supersolid phases occurring in conventional periodic lattices. For sufficiently large interaction strength and particle density, global condensation is lost and quantum exchanges are restricted to specific spatial regions. The emerging quantum phase is therefore a Bose glass, which here is stabilized in the absence of any source of disorder or quasidisorder, purely as a result of the interplay between quantum effects, particle interactions and quasicrystalline substrate. This finding clearly indicates that (quasi)disorder is not essential to observe Bose glass physics. Our results are of interest for ongoing experiments on (quasi)disorder-free quasicrystalline lattices.
We study the emergence of Bose glass phases in self sustained bosonic quasicrystals induced by a pair interaction between particles of Lifshitz–Petrich type. By using a mean-field variational method designed in momentum space as well as Gross–Pitaevskii simulations we determine the phase diagram of the model. The study of the local and global superfluid fraction allows the identification of supersolid, super quasicrystal, Bose glass and insulating phases. The Bose glass phase emerges as a quasicrystal phase in which the global superfluidity is essentially zero, while the local superfluidity remains finite in certain ring structures of the quasicrystalline pattern. Furthermore, we perform continuous space Path Integral Monte Carlo simulations for a case in which the interaction between particles stabilizes a quasicrystal phase. Our results show that as the strength of the interaction between particles is increased the system undergoes a sequence of states consistent with the super quasicrystal, Bose glass, and quasicrystal insulator thermodynamic phases.
We study the ground state phases of the Bose-Hubbard model with disordered potentials for quasicrystalline systems, with a focus on the Bose-Glass phase. Generally speaking, disorder can lead to the formation of a Bose-Glass, which is characterised by the lack of global phase coherence across the lattice. Here, we will look at two models; the interacting 2D Aubry-Andre model and disordered vertex models from quasicrystalline tiling patterns. Unlike typical disorder in homogeneous, periodic systems, quasicrystalline models possess self-similarity. This leads to a fascinating interplay between correlated, quasiperiodic order and uncorrelated, random disorder. In this work, we combine Gutzwiller mean-field theory with a percolation analysis of superfluid clusters, allowing the critical points and phase regions of these disordered systems to be mapped. When the long-range order is separate to the random disorder, as is the case for the disordered vertex models, then the physics reflects that of periodic lattices with disorder. However, we find that long-range order present in the disorder term of the 2D Aubry-Andre model can result in some peculiarities to the physics of the Bose-Glass. These peculiarities include stabilisation from weak disorder lines and intricate, ordered structures of the phase itself that may provide fruitful areas of future study.
The combined effect of disorder and interactions is central to the richness of condensed matter physics and can lead to novel quantum states such as the Bose glass phase in disordered bosonic systems. Here, we report on the experimental realisation of the two-dimensional Bose glass using ultra-cold atoms in an eight-fold symmetric quasicrystalline optical lattice. By probing the coherence properties of the system, we observe a Bose glass to superfluid transition and map out the phase diagram in the weakly interacting regime. Moreover, we reveal the non-ergodic nature of the Bose glass by probing the capability to restore coherence. Our observations are in good agreement with recent quantum Monte Carlo predictions and pave the way for experimentally testing the connection between the Bose glass, many-body localisation, and glassy dynamics more generally.
Deterministic quasiperiodicity in quantum systems has long been associated with localization, criticality, or glassy behavior, and has therefore been believed to suppress long-range order rather than stabilize it. Here we demonstrate the opposite: quasiperiodicity in interactions--without any quasiperiodic potential, disorder, or geometric modulation--can generate coherent, ordered quantum phases. We study hard-core bosons in one dimension with quasiperiodic long-range interactions, V_{ij}=V_0 \cos(παi)\cos(παj), where n=α=(\sqrt{5}-1)/2 is the inverse golden ratio. Using large-scale path-integral quantum Monte Carlo simulations, we uncover thermodynamically stable incompressible plateaus at irrational densities tied to Fibonacci ratios. These plateaus exhibit sharp incommensurate Bragg peaks, signaling an emergent quasi-solid with long-range quasicrystalline density order. More strikingly, at nearby fillings and interaction strengths, we identify a quasi-supersolid phase that supports both Fibonacci density ordering and finite superfluid density--demonstrating that interaction-induced quasiperiodicity can stabilize supersolid coherence. Our results establish a new mechanism for realizing ordered quasicrystalline quantum matter, and provide realistic guidance for implementation in Rydberg atom arrays, multimode cavity-QED systems, and trapped-ion quantum simulators.
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 2D quasiperiodic models. However, a quasicrystalline geometry is not sufficient to result in differences from crystalline realisations of the BG, whereas a quasiperiodic form of disorder can result in different physics, as we observe in the 2D AA model.
We report on results of quantum Monte Carlo simulations for bosons in a two-dimensional quasiperiodic optical lattice. We study the ground state phase diagram at unity filling and confirm the existence of three phases: superfluid, Mott insulator, and Bose glass. At lower interaction strength, we find that sizable disorder strength is needed in order to destroy superfluidity in favor of the Bose glass. On the other hand, at large enough interaction superfluidity is completely destroyed in favor of the Mott insulator (at lower disorder strength) or the Bose glass (at larger disorder strength). At intermediate interactions, the system undergoes an insulator to superfluid transition upon increasing the disorder, while a further increase of disorder strength drives the superfluid to Bose glass phase transition. While we are not able to discern between the Mott insulator and the Bose glass at intermediate interactions, we study the transition between these two phases at larger interaction strength and find no evidence of a Mott-glass-like behavior.