Numerical integration for ab initio many-electron self energy calculations within the GW approximation

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...

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Published inJournal of computational physics Vol. 286
Main Authors Liu, Fang, Lin, Lin, Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, Vigil-Fowler, Derek, Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, Lischner, Johannes, Kemper, Alexander F., Sharifzadeh, Sahar, Jornada, Felipe H. da, Deslippe, Jack, Yang, Chao
Format Journal Article
LanguageEnglish
Published United States 01.04.2015
Subjects
APPROXIMATIONS
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
COULOMB FIELD
ELECTRONS
GREEN FUNCTION
MANY-BODY PROBLEM
POLYNOMIALS
QUADRATURES
SELF-ENERGY
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Summary: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.
ISSN:0021-9991
1090-2716
DOI:10.1016/J.JCP.2015.01.023