论文标题
布里鲁因区域集成的自动，高阶和自适应算法
Automatic, high-order, and adaptive algorithms for Brillouin zone integration
论文作者
论文摘要
我们提出了具有非零但可能非常小的扩展因子$η$的有效方法，以使用Wannier插值进行有效评估的折叠式汉密尔顿人。我们描述了可靠的高阶准确算法自动化收敛到用户指定的错误公差$ \ varepsilon $，这强调了相对于$η$的有效计算缩放。在分析了适用于大扩张的标准equapaced集成方法之后，我们描述了一种在小$η$制度中有效的简单迭代自适应集成算法。它的计算成本量表将$ \ MATHCAL {o}（\ log^3（η^{ - 1}））$作为$η\ to 0^+$在三维中，而不是$ \ MATHCAL {O}（η^{ - 3}）$用于Equispaced集成。我们认为，相比之下，基于树的自适应集成方法仅为$ \ Mathcal {o}（\ log（η^{ - 1}）/η^{2}）$对于典型的Brillouin Zone积分。除了其有利的缩放率外，迭代的自适应算法很容易实现，尤其是在不可减至的布里鲁因区域集成，为此避免了基于树的方案所需的四面体网格。我们通过计算SRVO $ _3 $的光谱功能并在MEV量表上进行扩展来说明算法。
We present efficient methods for Brillouin zone integration with a non-zero but possibly very small broadening factor $η$, focusing on cases in which downfolded Hamiltonians can be evaluated efficiently using Wannier interpolation. We describe robust, high-order accurate algorithms automating convergence to a user-specified error tolerance $\varepsilon$, emphasizing an efficient computational scaling with respect to $η$. After analyzing the standard equispaced integration method, applicable in the case of large broadening, we describe a simple iterated adaptive integration algorithm effective in the small $η$ regime. Its computational cost scales as $\mathcal{O}(\log^3(η^{-1}))$ as $η\to 0^+$ in three dimensions, as opposed to $\mathcal{O}(η^{-3})$ for equispaced integration. We argue that, by contrast, tree-based adaptive integration methods scale only as $\mathcal{O}(\log(η^{-1})/η^{2})$ for typical Brillouin zone integrals. In addition to its favorable scaling, the iterated adaptive algorithm is straightforward to implement, particularly for integration on the irreducible Brillouin zone, for which it avoids the tetrahedral meshes required for tree-based schemes. We illustrate the algorithms by calculating the spectral function of SrVO$_3$ with broadening on the meV scale.
