Nonlinear eigenvalue algorithm for $GW$ quasiparticle equations

Abstract

The use of the Green's function in quantum many-body theory often leads to nonlinear eigenvalue problems, as the Green's function needs to be defined in the energy domain. The GW approximation method is one typical example. In this article, we introduce a method based on the FEAST eigenvalue algorithm for accurately solving the nonlinear eigenvalue G0W0 quasiparticle equation. Based on the FEAST contour integral method for nonlinear eigenvalue problems, the energy (eigenvalue) domain is extended to the complex plane. An analytic continuation is introduced to the calculation of the GW self-energy to carry the imaginary parts of both Green's functions and FEAST contour quadrature nodes. Calculation results for various molecules are presented and compared with the more conventional graphical solution approximation method and spectral functions method. It is confirmed that the highest occupied molecular orbital from the Kohn-Sham (and Hartree-Fock) equation is very close to that of GW, while the lowest unoccupied molecular orbital shows noticeable differences.

arXiv commentv2: Title changed to match the published version in Phys. Rev. B 111, 045137 (2025). Corrected an error in Eq. 12 and section [CD method + FEAST] and clarified the corresponding discussion. These corrections do not affect the main conclusions; Eq. 12 was a typo and section [CD method + FEAST] affects calculation method but does not affect the correct nonlinear eigenvalue algorithm and results