主 题: Computational and Applied Math Seminar——Computational issues in the GW approximation
报告人: Fang Liu (School of Statistics and Mathematics, Central University of Finance and Economics)
时 间: 2017-12-05 15:00-16:00
地 点: Room 1309, Sciences Building No. 1
Abstract: In the Green's function formalism of a many-body perturbation theory, the excitation of the material is described in terms of quasi-particle energies (eigenvalues) of a single-particle Hamiltonian that contains a self energy term. We will talk about two computational issues in the GW approximation of the self energy. Firstly, the computation of dielectric matrix is important in the GW approximation. The standard method to compute dielectric matrix requires information of thousands of empty states which is very demanding. Hence an alternative method was proposed to overcome this problem by solving the so called Sternheimer equation. The challenges and current progress of solving the Sternheimer equation will be introduced. Secondly, due to the presence of singularities in the integrand for the convolution of a Green’s function with a screened Coulomb potential on the real axis, the numerical convolution must be carried out with care. We present a numerical integration scheme for evaluating this convolution. Both theoretical analysis and numerical examples show that this scheme is more reliable and accurate than the standard quadrature rules such as the trapezoidal rule.
This is a joint work with Chao Yang, Lin Lin, Meiyue Shao, Lex Kemper, Jack Deslippe, Jeffrey Neaton’s group, and Steven Louie’s group.
[1] Fang Liu, Lin Lin, Derek Vigil-Fowler, Johannes Lischner, Alexander F. Kemper, Sahar Sharifzadeh, Felipe H. da Jornada, Jack Deslippe, Chao Yang, Jeffrey B. Neaton , Steven G. Louie, Numerical integration for ab initio many-electron self energy calculations within the GW approximation, Journal of Computational Physics, 286, 1-13, 2015.
[2] MeiYue Shao, Lin Lin, Chao Yang, Fang Liu, Felipe H. Da Jornada, Jack Deslippe, Steven G. Louie, Low rank approximation in G0W0 calculations, Science China Mathematics, 59 (8), 1593–1612, 2016.
[3] Michiel J. van Setten, Fabio Caruso, Sahar Sharifzadeh, Xinguo Ren, Matthias Scheffler, Fang Liu, Johannes Lischner, Lin Lin, Jack R. Deslippe, Steven G. Louie, Chao Yang, Florian Weigend, Jeffrey B. Neaton, Ferdinand Evers, and Patrick Rinke, GW100: Benchmarking G0W0 for Molecular Systems, Journal of Chemical Theory and Computation, 11, 5665?5687, 2015.
简介：刘芳，中央财经大学统计与威廉希尔教授。先后于1999年和2002年毕业于湘潭大学数学系，分别获理学学士学位和硕士学位。2006年毕业于中国科学院数学与系统科学研究院计算数学与科学工程计算研究所，获理学博士学位。曾获中国科学院数学与系统科学研究院经理奖学金优秀奖（2005），被评为中国科学院数学与系统科学研究院三好员工（2006）。2006年进入中央财经大学任教。曾被评为中央财经大学十佳班主任（2007），并获中央财经大学成心教师优秀学术奖（2011）、涌金教师优秀学术奖（2012）、成心优秀教学奖（2013）和基础课教学奖（2009，2017）。2012年9月至2014年8月，在美国劳伦斯伯克利国家实验室计算研究系进行访问交流。目前主要研究方向是第一原理计算领域的高效数值算法、软件开发以及材料性质模拟和预测。已在主流数学、物理国际学术期刊上发表论文十余篇。
