论文标题
在六角形金色瓷砖上的哈伯德模型中的铁磁有序状态
Ferrimagnetically ordered states in the Hubbard model on the hexagonal golden-mean tiling
论文作者
论文摘要
我们研究了二维六边形金均值瓷砖上半填充哈伯德模型的磁性。我们发现，瓷砖的顶点模型是双分的，具有$ \ sqrt {5}/（6τ^3）$（$τ$是黄金平均值）的sublatice失衡，并且非交互紧密结合模型可在$ e = 0 $ e = 0 $ $ e = 0 $ = 0 $中均可进行宏观变性。我们澄清说，每个sublattice都有特定类型的限制状态，这又导致弱耦合方案中局部磁性的有趣空间模式。此外，这使我们能够分析地在受限状态的分数上以$（τ+9）/（6τ^6）\ sim 0.0986 $的形式获得下限，这是确定的确切分数。这些结果表明，即使在弱耦合极限下，也实现了铁磁性有序状态。库仑相互作用的引入提高了费米水平的宏观退化，并引起有限的交错磁化以及均匀的磁化。同样，磁化的空间分布随着相互作用强度的增加而连续变化。还根据垂直空间分析解决了磁有序状态的交叉行为。
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.
