论文标题
准晶体系统中的平均场玻色玻璃
The Mean-Field Bose Glass in Quasicrystalline Systems
论文作者
论文摘要
我们确认在2D准晶体玻色 - 哈贝型模型中存在平均玻璃玻璃。我们关注两个模型，在这些模型中，问题的不同部分都存在。首先，我们考虑了Aubry-André模型的2D概括，其中晶格的几何形状是具有准隔层电位的正方形的。其次，我们考虑了随机无序的顶点模型，该模型采用具有非晶体旋转对称性的高等瓷砖，并从瓷砖的顶点和长度形成晶格。对于无序的顶点模型，平均场玻色玻璃在化学势的大范围内形成，我们观察到与随机均匀疾病的方格没有显着差异。临界点在准晶体和结晶晶格几何之间存在随机障碍的情况下，可以通过不同的配位数和存在不同的旋转对称性来解释。在2d Aubry-André模型中，从晶体无序系统的通常相图中观察到了实质性差异。我们表明，可以从潜在的电位预测弱调制线，并且可以在某些方向上稳定或抑制平均场玻色玻璃。这导致在2D Aubry-André模型中的平均田间玻璃玻璃的叶状结构，该结构与随机疾病的情况显着不同。在这项工作中研究的两个准晶模型共同存在，如2D准膜模型所预期的那样，存在平均场玻色玻璃相。然而，准晶几何形状不足以导致与玻色玻璃的结晶实现的差异，而正常疾病的准碘形式可能会导致不同的物理学，正如我们在2d aubry-andré模型中所观察到的那样。
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-André 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-André 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-André 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-André model.
