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Title: 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 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.
Authors:
 [1] ;  [2] ;  [3] ;  [4] ;  [3] ;  [4] ;  [3] ;  [5] ;  [6] ;  [4] ;  [3] ;  [7] ;  [5] ;
  1. School of Statistics and Mathematics, Central University of Finance and Economics, Beijing 100081 (China)
  2. Department of Mathematics, University of California, Berkeley, CA 94720 (United States)
  3. (United States)
  4. Department of Physics, University of California, Berkeley, CA 94720 (United States)
  5. Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States)
  6. Department of Electrical and Computer Engineering and Division of Materials Science and Engineering, Boston University, Boston, MA 02215 (United States)
  7. NERSC, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States)
Publication Date:
OSTI Identifier:
22465613
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 286; Other Information: Copyright (c) 2015 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; COULOMB FIELD; ELECTRONS; GREEN FUNCTION; MANY-BODY PROBLEM; POLYNOMIALS; QUADRATURES; SELF-ENERGY