论文标题
一个简单的真实空间方案，适用于定期狄拉克操作员
A simple real-space scheme for periodic Dirac operators
论文作者
论文摘要
我们在这项工作中解决了二维定期狄拉克汉顿人离散化的问题。矩形网格上的标准有限差异方法困扰着所谓的费米昂加倍问题，这会产生虚假的非物理模式。物理社区中使用的困难的古典方式是在傅立叶空间中工作，这是不需要计算哈密顿量和相关卷积中系数的傅立叶分解。我们在这项工作中提出了一种简单的真实空间方法，可免疫费用加倍问题，并适用于所有二维周期性晶格。该方法基于光谱分化技术。我们将数值方案应用于受周期性磁场和扭曲的双层石墨烯中的石墨烯中平坦带的研究。
We address in this work the question of the discretization of two-dimensional periodic Dirac Hamiltonians. Standard finite differences methods on rectangular grids are plagued with the so-called Fermion doubling problem, which creates spurious unphysical modes. The classical way around the difficulty used in the physics community is to work in the Fourier space, with the inconvenience of having to compute the Fourier decomposition of the coefficients in the Hamiltonian and related convolutions. We propose in this work a simple real-space method immune to the Fermion doubling problem and applicable to all two-dimensional periodic lattices. The method is based on spectral differentiation techniques. We apply our numerical scheme to the study of flat bands in graphene subject to periodic magnetic fields and in twisted bilayer graphene.
