论文标题
用于准晶体电势的哈伯德模型
Hubbard Models for Quasicrystalline Potentials
论文作者
论文摘要
准晶体是长期订购的，但不是周期性的，因此对凝聚态物理学提出了令人着迷的挑战，因为人们无法根据Bloch的定理求助于通常的工具箱。在这里，我们提出了一种数值方法，用于在不使用Bloch定理的情况下构建非周期性电势的哈伯族哈密顿量，并将其应用于最近使用冷原子实现的八倍旋转对称的2D光学准晶体。我们构建了最大局部的Wannier功能，并使用它们来提取现场能量，隧道振幅和相互作用能。此外，我们介绍了一个配置空间表示，其中以形状和局部环境订购了站点，从而导致对无限大小的准晶体的紧凑描述，其中所有汉密尔顿参数都可以表达为平滑函数。此配置空间图片使人们可以为数值多体计算构建任意大型的紧密结合图，并实现有关这些模型的拓扑结构和多体物理学的新分析论证，例如，该Quasicrystal将在热力学限制中托管单位填充单位填充的Mott Mott绝缘子。
Quasicrystals are long-range ordered, yet not periodic, and thereby present a fascinating challenge for condensed matter physics, as one cannot resort to the usual toolbox based on Bloch's theorem. Here, we present a numerical method for constructing the Hubbard Hamiltonian of non-periodic potentials without making use of Bloch's theorem and apply it to the case of an eightfold rotationally symmetric 2D optical quasicrystal that was recently realized using cold atoms. We construct maximally localised Wannier functions and use them to extract on-site energies, tunneling amplitudes, and interaction energies. In addition, we introduce a configuration-space representation, where sites are ordered in terms of shape and local environment, that leads to a compact description of the infinite-size quasicrystal in which all Hamiltonian parameters can be expressed as smooth functions. This configuration-space picture allows one to construct arbitrarily large tight-binding graphs for numerical many-body calculations and enables new analytic arguments on the topological structure and many-body physics of these models, for instance the conclusion that this quasicrystal will host unit-filling Mott insulators in the thermodynamic limit.
