Hubbard models for quasicrystalline potentials
Hubbard models for quasicrystalline potentials
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DOI：
10.1103/physrevb.107.144202
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发表时间：
2022-10
影响因子：
3.7
通讯作者：
E. Gottlob;U. Schneider
中科院分区：
文献类型：
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作者：
E. Gottlob;U. Schneider
准晶体是长程有序的，但不是周期性的，因此对凝聚态物理学提出了一个迷人的挑战，因为人们不能求助于基于布洛赫定理的常用工具箱。本文提出了一种不使用布洛赫定理构造非周期势的哈伯德哈密顿量的数值方法，并将其应用于最近使用冷原子实现的八重旋转对称二维光学准晶体的情况。我们构建了最大局部化的万尼尔函数，并利用它们来提取现场能量、隧道振幅和相互作用能量。此外，我们引入了一种构型空间表示，其中位置根据形状和局部环境排序，这导致了无限大小准晶体的紧凑描述，其中所有哈密顿参数都可以表示为光滑函数。这种构型空间图允许人们为数值多体计算构建任意大的紧密结合图，并为这些模型的拓扑结构和多体物理提供了新的解析论据，例如，在热力学极限下，准晶体将承载单元填充莫特绝缘体的结论。
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.