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. Neaton; Steven G. Louie

doi:10.1016/j.jcp.2015.01.023

arXiv · 1402.5433

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. Neaton·Steven G. Louie

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Abstract

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.

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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. 2014-02-21. Numerical integration for ab initio many-electron self energy calculations within the GW approximation. https://doi.org/10.1016/j.jcp.2015.01.023

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