Numerical integration for ab initio many-electron self energy calculations within the GW approximation
Fang Liu, Lin Lin, Derek Vigil-Fowler, Johannes Lischner, Alexander F. Kemper, Sahar Sharifzadeh, Felipe Homrich da Jornada, Jack Deslippe, Chao Yang, Jeffrey B… 展开作者
Fang Liu, Lin Lin, Derek Vigil-Fowler, Johannes Lischner, Alexander F. Kemper, Sahar Sharifzadeh, Felipe Homrich da Jornada, Jack Deslippe, Chao Yang, Jeffrey B. Neaton, Steven G. Louie
We present a numerical integration scheme for evaluating the convolution of a Green's function with a screened Coulomb potential on the real axis in the GW approximation of the self energy. Our scheme takes the zero broadening limit in Green's function first, replaces the numerator of the integrand with a piecewise polynomial approximation, and performs principal value integration on subintervals analytically. We give the error bound of our numerical integration scheme and show by numerical examples that it is more reliable and accurate than the standard quadrature rules such as the composite trapezoidal rule. We also discuss the benefit of using different self energy expressions to perform the numerical convolution at different frequencies.
A comment on "Ab initio calculations of pressure-dependence of high-order elastic constants using finite deformations approach" by I. Mosyagin, A.V. Lugovskoy, O.M. Krasilnikov, Yu.Kh. Vekilov, S.I. Simak and I.A. Abrikosov
Efficient ab initio many-body calculations based on sparse modeling of Matsubara Green's function
本课堂讲稿回顾了最近提出的基于格林函数数据压缩的有效从头计算多体计算的稀疏建模方法。稀疏建模技术是基于一个紧凑的正交基，一个中间表示（IR）的基础上，时间和松原格林函数。基于IR基的稀疏采样方法可以有效地求解图解方程。我们描述了IR基的基本性质，稀疏采样方法及其在基于GW近似和Migdal-Eliashberg理论的从头计算中的应用。我们还描述了一个数值库的IR基础和稀疏采样方法，稀疏IR，并提供其示例代码。这份课堂讲稿是在日文评论文章的基础上做了重大修改[H. Shinaoka等人，Solid State Physics 56（6），301（2021）]。
Efficient "on-the-fly" calculation of Raman spectra from \textit{ab-initio} molecular dynamics: Application to hydrophobic/hydrophilic solutes in bulk water
