Full-frequency GW without frequency
Full-frequency GW without frequency
复制标题
DOI：
10.1063/5.0035141
复制
发表时间：
2021-01-28
影响因子：
4.4
通讯作者：
Berkelbach, Timothy C.
中科院分区：
文献类型：
--
作者：
Bintrim, Sylvia J.;Berkelbach, Timothy C.
GW 近似的高效计算机实现必须逼近数值上具有挑战性的频率积分；积分可以通过分析方式执行，但这样做会导致昂贵的实现，其计算成本为 O(N-6)，其中 N 是系统的大小。在这里，我们引入了全频 GW 近似的新公式，将其精确地重新转换为扩展空间中的特征值问题。这种新公式 (1) 避免使用时间或频率网格，(2) 自然地消除了对常见“对角线”近似的需要，(3) 支持通用迭代本征求解器，将规范缩放减少到 O(N-5)，(4) 实现密度拟合实现，将缩放减少到 O(N-4)。我们对这些缩放行为进行了数值验证，并测试了由这种新公式激发的各种近似值。人们发现新的公式与基于解析延拓或轮廓变形的传统 O(N-4) 方法具有竞争力。在这个新的公式中，GW近似与构型相互作用、耦合簇理论和代数图解构造的关系变得尤为明显，为GW近似的改进提供了新的方向。
Efficient computer implementations of the GW approximation must approximate a numerically challenging frequency integral; the integral can be performed analytically, but doing so leads to an expensive implementation whose computational cost scales as O(N-6), where N is the size of the system. Here, we introduce a new formulation of the full-frequency GW approximation by exactly recasting it as an eigenvalue problem in an expanded space. This new formulation (1) avoids the use of time or frequency grids, (2) naturally obviates the need for the common "diagonal" approximation, (3) enables common iterative eigensolvers that reduce the canonical scaling to O(N-5), and (4) enables a density-fitted implementation that reduces the scaling to O(N-4). We numerically verify these scaling behaviors and test a variety of approximations that are motivated by this new formulation. The new formulation is found to be competitive with conventional O(N-4) methods based on analytic continuation or contour deformation. In this new formulation, the relation of the GW approximation to configuration interaction, coupled-cluster theory, and the algebraic diagrammatic construction is made especially apparent, providing a new direction for improvements to the GW approximation.