六角金均值镶嵌上哈伯德模型的亚铁磁有序态
Ferrimagnetically ordered states in the Hubbard model on the hexagonal golden-mean tiling
摘要：
研究了二维六角金均值镶嵌上半填充哈伯德模型的磁性。我们发现，顶点模型的平铺是二分的，与$\sqrt{5}/(6τ^3)$（其中$τ$是黄金分割）的亚晶格不平衡，和非相互作用的紧束缚模型给出宏观简并态在$E=0$。我们澄清，每个子晶格有特定类型的受限状态，这反过来又导致了一个有趣的空间图案在弱耦合制度的局部磁化。此外，这使我们能够解析地获得上的分数的限制态的下限为$(τ+9)/(6τ^6)\sim 0.0986$，这是被证明是确切的分数。这些结果表明，亚铁磁有序状态，即使在弱耦合限制实现。库仑相互作用的引入提高了费米能级的宏观简并度，在均匀磁化的同时也产生了有限的交错磁化。同样，磁化强度的空间分布随着相互作用强度的增加而连续变化。在磁有序态的交叉行为也解决了在垂直空间分析。
英文摘要：
We study magnetic properties of the half-filled Hubbard model on the two-dimensional hexagonal golden-mean tiling. We find that the vertex model of the tiling is bipartite, with a sublattice imbalance of $\sqrt{5}/(6τ^3)$ (where $τ$ is the golden mean), and that the non-interacting tight-binding model gives macroscopically degenerate states at $E=0$. We clarify that each sublattice has specific types of confined states, which in turn leads to an interesting spatial pattern in the local magnetizations in the weak coupling regime. Furthermore, this allows us to analytically obtain the lower bound on the fraction of the confined states as $(τ+9)/(6τ^6)\sim 0.0986$, which is conjectured to be the exact fraction. These results imply that a ferrimagnetically ordered state is realized even in the weak coupling limit. The introduction of the Coulomb interaction lifts the macroscopic degeneracy at the Fermi level, and induces finite staggered magnetization as well as uniform magnetization. Likewise, the spatial distribution of the magnetizations continuously changes with increasing interaction strength. The crossover behavior in the magnetically ordered states is also addressed in terms of the perpendicular space analysis.
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