论文标题
在Ammann-Beenker瓷砖上的Hubbard模型中的抗磁性有序状态中的超晶格结构
Superlattice structure in the antiferromagnetically ordered state in the Hubbard model on the Ammann-Beenker tiling
论文作者
论文摘要
我们研究了Ammann-Beenker瓷砖上半填充的Hubbard模型中的磁性。首先，我们专注于具有局部八倍旋转对称性的域结构，以检查紧密结合模型的严格局部限制状态。我们计算系统上由通缩操作产生的较大域中的顶点和受限状态的数量。然后，在弱耦合极限中对磁性发挥重要作用的受限状态的分数被以$ p = 1/2τ^2 $获得，其中$τ（= 1+\ sqrt {2}）$是银比。还发现，封闭状态的波函数密集分布在系统中，从而引入了库仑相互作用，立即引起有限的交错磁化。增加了库仑相互作用，磁化的空间分布不断地变为海森堡模型的空间分布。我们讨论了垂直空间表示中的跨界行为，并揭示了交错磁化的空间分布中的超晶格结构。
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.
