Nonuniform grids for Brillouin zone integration and interpolation
Nonuniform grids for Brillouin zone integration and interpolation
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DOI：
10.1103/physrevb.106.155102
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发表时间：
2022-08
影响因子：
3.7
通讯作者：
Siyu Chen;Pascal T. Salzbrenner;B. Monserrat
中科院分区：
文献类型：
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作者：
Siyu Chen;Pascal T. Salzbrenner;B. Monserrat
我们提出了函数在布里渊区上的数值积分的两个发展。首先，我们引入了一个非均匀网格，我们称之为Farey网格，它是常规网格的推广。其次，我们引入了适应对称的Voronoi镶嵌，这是一种为任意网格中的点分配权重的通用技术。结合这两个发展，我们提出了一种执行布里渊区域积分和插值的策略，与基于规则均匀网格的常规方法相比，该策略提供了显着的计算优势。我们在第一性原理计算的背景下，通过研究石墨烯和MgB2声子色散中的Kohn异常，以及评估电子-声子驱动的金刚石和铋带隙重整化，展示了我们的方法。在声子计算中，当使用密度泛函微扰理论时，我们发现速度增加了3到4倍，当使用有限差分与超级细胞结合时，速度增加了6到7倍。因此，密度泛函微扰理论与有限差分理论之间的计算费用具有可比性。对于电子-声子耦合计算，我们发现了更大的加速。最后，我们还证明了Farey网格可以表示为广泛使用的规则网格的组合，这应该有助于该方法的采用。
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.