论文标题
布里鲁因区域集成和插值的不均匀网格
Nonuniform grids for Brillouin zone integration and interpolation
论文作者
论文摘要
我们提供了两个发展，用于在布里鲁因区域上函数的数值集成。首先，我们引入了一个不均匀的网格，我们将其称为Farey Grid，该网格概括了常规网格。其次，我们介绍了对称性适应的Voronoi Tessellation，这是一种通用技术，可将权重分配给任意网格中的点。结合了这两个发展，我们提出了一种执行布里鲁因区域集成和插值的策略，该策略与基于常规统一网格的常规方法相比，提供了显着的计算优势。我们通过研究石墨烯和MGB2的声子分散体以及对钻石和bismuthene的频带驱动的频带差异的评估，在第一原理计算的背景下证明了我们的方法。在声子计算中，当使用密度功能扰动理论时，我们发现加速度为3至4，而使用有限差异与超级电池结合使用时，加速度为6至7。结果，密度功能扰动理论与有限差异之间的计算费用变得可比。对于电子波耦合计算，我们发现更大的加速度。最后，我们还证明了Farey网格可以表示为广泛使用的常规网格的组合，这应该有助于采用这种方法。
We present two developments for the numerical integration of a function over the Brillouin zone. First, we introduce a nonuniform grid, which we refer to as the Farey grid, that generalizes regular grids. Second, we introduce symmetry-adapted Voronoi tessellation, a general technique to assign weights to the points in an arbitrary grid. Combining these two developments, we propose a strategy to perform Brillouin zone integration and interpolation that provides a significant computational advantage compared to the usual approach based on regular uniform grids. We demonstrate our methodology in the context of first principles calculations with the study of Kohn anomalies in the phonon dispersions of graphene and MgB2, and in the evaluation of the electron-phonon driven renormalization of the band gaps of diamond and bismuthene. In the phonon calculations, we find speedups by a factor of 3 to 4 when using density functional perturbation theory, and by a factor of 6 to 7 when using finite differences in conjunction with supercells. As a result, the computational expense between density functional perturbation theory and finite differences becomes comparable. For electron-phonon coupling calculations we find even larger speedups. Finally, we also demonstrate that the Farey grid can be expressed as a combination of the widely used regular grids, which should facilitate the adoption of this methodology.
