标题： 调制的蜂窝晶格及其磁性属性 显示英文标题

标题： Modulated honeycomb lattices and their magnetic properties

摘要： 我们提出了一类调制蜂窝晶格，这是一类由金属平均数表征的准周期镶嵌结构。这些晶格由六个不同的六边形原型组成，具有两种边长，$\ell$和$s$，可以被视为蜂窝晶格的连续变形。通过其替代规则来研究其结构特性。为了研究电子特性，我们在这些镶嵌结构上构建了一个紧束缚模型，引入了两种类型的跃迁积分，$t_L$和$t_S$，分别对应于两种边长，$\ell$和$s$。通过对这些准周期镶嵌结构上的哈密顿量进行对角化，我们计算了相应的态密度（DOS）。我们的分析表明，在跃迁积分分布中引入准周期性会在较高能量处导致DOS出现尖峰结构，而在较低能量处的线性DOS（$E\sim 0$）保持稳定。这与无序紧束缚模型中的平滑DOS形成对比，在无序紧束缚模型中，两种类型的跃迁积分根据给定的比例随机分布。此外，我们通过实空间哈特里近似方法研究了在调制蜂窝晶格上的Hubbard模型的磁特性。由于费米能级处不存在非相互作用的DOS，因此在有限的相互作用强度下会发生磁相变。 当$t_L\sim t_S$时，相变点主要由线性 DOS 控制。 然而，远离条件$t_L=t_S$时，准周期结构在降低临界相互作用强度方面起着重要作用，这与无序系统形成对比。 通过垂直空间分析，我们证明准周期铺砌中固有的亚晶格不对称性出现在磁性剖面中，为准周期性和电子关联之间的相互作用提供了见解。 显示英文摘要

摘要： We propose a family of modulated honeycomb lattices, a class of quasiperiodic tilings characterized by the metallic mean. These lattices consist of six distinct hexagonal prototiles with two edge lengths, $\ell$ and $s$, and can be regarded as a continuous deformation of the honeycomb lattice. The structural properties are examined through their substitution rules. To study the electronic properties, we construct a tight-binding model on the tilings, introducing two types of hopping integrals, $t_L$ and $t_S$, corresponding to the two edge lengths, $\ell$ and $s$, respectively. By diagonalizing the Hamiltonian on these quasiperiodic tilings, we compute the corresponding density of states (DOS). Our analysis reveals that the introduction of quasiperiodicity in the distribution of hopping integrals induces a spiky structure in the DOS at higher energies, while the linear DOS at low energies ($E\sim 0$) remains robust. This contrasts with the smooth DOS in the disordered tight-binding model, where two types of hopping integrals are randomly distributed according to a given ratio. Furthermore, we study the magnetic properties of the Hubbard model on modulated honeycomb lattices by means of real-space Hartree approximations. A magnetic phase transition occurs at a finite interaction strength due to the absence of the noninteracting DOS at the Fermi level. When $t_L\sim t_S$, the phase transition point is primarily governed by the linear DOS. However, far from the condition $t_L=t_S$, the quasiperiodic structure plays a significant role in reducing the critical interaction strength, which is in contrast to the disordered system. Using perpendicular space analysis, we demonstrate that sublattice asymmetry inherent in the quasiperiodic tilings emerges in the magnetic profile, providing insights into the interplay between quasiperiodicity and electronic correlations.