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  • Letter
  • Open Access

Normalization of exact quasiparticle wave functions in the Green's function method guaranteed by the Ward identity

Takeru Nakashima, Hannes Raebiger, and Kaoru Ohno*

  • Department of Physics, Yokohama National University, 79-5 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan

  • *ohno@ynu.ac.jp
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Phys. Rev. B 104, L201116 – Published 29 November, 2021

DOI: https://doi.org/10.1103/PhysRevB.104.L201116

Abstract

It has been a long-standing problem in N-electron systems as to how to solve the Dyson equation with the quasiparticle wave functions defined as 〈Ψ0N|ψs(r)|ΨνN+1〉 and 〈ΨμN−1|ψs(r)|Ψ0N〉, which are not mutually orthogonal and have a norm less than 1. We show that quasiparticle wave functions without multiple excitations can exactly be normalized to unity owing to the Ward identity and the vertex function in (q,ω′−ω)→0, although they are not necessarily mutually orthogonal. Since they satisfy an eigenvalue equation with the hermitized self-energy due to Baym-Kadanoff's conservation laws, the present theory can be regarded as an extension of the Kohn-Sham density functional theory, with correlated, interacting, one-electron orbitals.

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Phys. Rev. B 104, L201116– Published 29 November, 2021
  • Received 10 August 2020
  • Revised 7 October 2020
  • Accepted 8 November 2021
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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