体半导体系统完全自洽GW计算中对角G和子空间W近似的分析
Analysis of diagonal G and subspace W approximations within fully self-consistent GW calculations for bulk semiconducting systems
摘要：
完全自洽GW（sc-GW）方法现在可用于评估各种分子和体系统的准粒子和光谱性质。然而，基于G和W的全矩阵的这种技术在计算上是苛刻的。常规使用的单次GW近似（G 0 W 0）对初始交换相关泛函的选择有不期望的依赖性。在文献中，许多所谓的自洽GW方法都是基于G的对角逼近和W的低阶逼近。因此，与全矩阵方法相比，检查这种近似值有多好是值得的。在这项工作中，我们认为铝砷，铝磷，镓磷，和ZnS作为原型系统进行SC-GW计算表示使用平面波基组的全G矩阵。我们将我们的sc-GW结果与对角G和子空间W近似的sc-GW结果（sc-GW-diagG和sc-GW-subW方法）进行了比较。在sc-GW-diagG方法中，相互作用G在非相互作用G的本征向量中展开，使得仅保留对角元素，而在sc-GW-subW计算中截断本征模的数量。从上述技术获得的结果进行了系统的分析。近似和全矩阵sc-GW方法之间的准粒子带隙的差异大多小于1.7%，这验证了这种广泛采用的近似，并且还显示了这种低等级近似如何用于包括高阶项，如顶点校正。
英文摘要：
Fully self-consistent GW (sc-GW) methods are now available to evaluate quasiparticle and spectral properties of various molecular and bulk systems. However, such techniques based on the full matrix of G and W are computationally demanding. The routinely used single-shot GW-approximation (G0W0) has an undesirable dependency on the choice of initial exchange-correlation functional. In the literature, many so-called self-consistent GW methods are based on diagonal approximation of G and low-ranking approximation of W. It is thus worth to check how good such approximations are in comparison with the full matrix method. In this work, we consider AlAs, AlP, GaP, and ZnS as the prototype systems to perform sc-GW calculations by expressing the full G matrix using a plane-wave basis set. We compared our sc-GW results with the diagonal G and subspace W approximated sc-GW results (sc-GW-diagG and sc-GW-subW methods). In the sc-GW-diagG method, interacting G is expanded in the eigenvectors of non-interacting G such that only diagonal elements are retained, whereas, the number of eigenmodes is truncated in sc-GW-subW calculations. A systematic analysis of the results obtained from the above techniques is presented. The differences in the quasiparticle bandgap between the approximated and the full matrix sc-GW approaches are mostly less than 1.7% that validates such widely adopted approximations, and also shows how such low-ranking approximation can be used to include higher-order terms like the vertex correction.
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