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

• Published in: Journal 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
• Language: English
• 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
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/J.JCP.2015.01.023

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.