Ammann-Beenker镶嵌上哈伯德模型反铁磁有序态的超晶格结构
Superlattice structure in the antiferromagnetically ordered state in the Hubbard model on the Ammann-Beenker tiling
摘要：
我们研究了Ammann-Beenker镶嵌上半填充哈伯德模型的磁性。首先，我们聚焦于具有局部八重旋转对称性的畴结构来研究紧束缚模型的严格定域受限态。我们系统地计算了收缩操作产生的较大区域中的顶点数和受限态数。然后，限制态的分数，这起着重要的作用，在弱耦合极限的磁性能，获得为$p=1/2τ^2$，其中$τ(=1+\sqrt{2})$是银的比例。研究还发现，束缚态的波函数在系统中分布较密，库仑相互作用的引入立即引起有限的交错磁化。随着库仑相互作用的增加，磁化强度的空间分布不断向海森堡模型的方向变化。我们讨论了垂直空间表象中的交叉行为，揭示了交错磁化空间分布中的超晶格结构。
英文摘要：
We study magnetic properties in the half-filled Hubbard model on the Ammann-Beenker tiling. First, we focus on the domain structure with locally eightfold rotational symmetry to examine the strictly localized confined states for the tightbinding model. We count the number of vertices and confined states in the larger domains generated by the deflation operations systematically. Then, the fraction of the confined states, which plays an important role for magnetic properties in the weak coupling limit, is obtained as $p=1/2τ^2$, where $τ(=1+\sqrt{2})$ is the silver ratio. It is also found that the wave functions for confined states are densely distributed in the system and thereby the introduction of the Coulomb interactions immediately induces the finite staggered magnetizations. Increasing the Coulomb interactions, the spatial distribution of the magnetizations continuously changes to those of the Heisenberg model. We discuss crossover behavior in the perpendicular space representation and reveal the superlattice structure in the spatial distribution of the staggered magnetizations.
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