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Title: One-particle many-body Green’s function theory: Algebraic recursive definitions, linked-diagram theorem, irreducible-diagram theorem, and general-order algorithms

A thorough analytical and numerical characterization of the whole perturbation series of one-particle many-body Green’s function (MBGF) theory is presented in a pedagogical manner. Three distinct but equivalent algebraic (first-quantized) recursive definitions of the perturbation series of the Green’s function are derived, which can be combined with the well-known recursion for the self-energy. Six general-order algorithms of MBGF are developed, each implementing one of the three recursions, the ΔMPn method (where n is the perturbation order) [S. Hirata et al., J. Chem. Theory Comput. 11, 1595 (2015)], the automatic generation and interpretation of diagrams, or the numerical differentiation of the exact Green’s function with a perturbation-scaled Hamiltonian. They all display the identical, nondivergent perturbation series except ΔMPn, which agrees with MBGF in the diagonal and frequency-independent approximations at 1 ≤ n ≤ 3 but converges at the full-configuration-interaction (FCI) limit at n=∞ (unless it diverges). Numerical data of the perturbation series are presented for Koopmans and non-Koopmans states to quantify the rate of convergence towards the FCI limit and the impact of the diagonal, frequency-independent, or ΔMPn approximation. The diagrammatic linkedness and thus size-consistency of the one-particle Green’s function and self-energy are demonstrated at any perturbation order on the basismore » of the algebraic recursions in an entirely time-independent (frequency-domain) framework. The trimming of external lines in a one-particle Green’s function to expose a self-energy diagram and the removal of reducible diagrams are also justified mathematically using the factorization theorem of Frantz and Mills. Equivalence of ΔMPn and MBGF in the diagonal and frequency-independent approximations at 1 ≤ n ≤ 3 is algebraically proven, also ascribing the differences at n = 4 to the so-called semi-reducible and linked-disconnected diagrams« less
ORCiD logo [1] ;  [1] ; ORCiD logo [2] ;  [3]
  1. Univ. of Illinois, Urbana-Champaign, IL (United States). Dept. of Chemistry
  2. Cardiff Univ., Park Place, Cardiff (United Kingdom). School of Chemistry
  3. Auburn Univ., AL (United States). Dept. of Chemistry and Biochemistry
Publication Date:
Grant/Contract Number:
FG02-11ER16211; SC0006028; FG02-12ER46875
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 147; Journal Issue: 4; Journal ID: ISSN 0021-9606
American Institute of Physics (AIP)
Research Org:
Univ. of Illinois, Urbana-Champaign, IL (United States)
Sponsoring Org:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); National Science Foundation (NSF); CREST, Japan Science and Technology Agency
Country of Publication:
United States
OSTI Identifier:
Alternate Identifier(s):
OSTI ID: 1372946