Oneparticle manybody Green’s function theory: Algebraic recursive definitions, linkeddiagram theorem, irreduciblediagram theorem, and generalorder algorithms
A thorough analytical and numerical characterization of the whole perturbation series of oneparticle manybody Green’s function (MBGF) theory is presented in a pedagogical manner. Three distinct but equivalent algebraic (firstquantized) recursive definitions of the perturbation series of the Green’s function are derived, which can be combined with the wellknown recursion for the selfenergy. Six generalorder 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 perturbationscaled Hamiltonian. They all display the identical, nondivergent perturbation series except ΔMPn, which agrees with MBGF in the diagonal and frequencyindependent approximations at 1 ≤ n ≤ 3 but converges at the fullconfigurationinteraction (FCI) limit at n=∞ (unless it diverges). Numerical data of the perturbation series are presented for Koopmans and nonKoopmans states to quantify the rate of convergence towards the FCI limit and the impact of the diagonal, frequencyindependent, or ΔMPn approximation. The diagrammatic linkedness and thus sizeconsistency of the oneparticle Green’s function and selfenergy are demonstrated at any perturbation order on the basismore »
 Authors:

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 Univ. of Illinois, UrbanaChampaign, IL (United States). Dept. of Chemistry
 Cardiff Univ., Park Place, Cardiff (United Kingdom). School of Chemistry
 Auburn Univ., AL (United States). Dept. of Chemistry and Biochemistry
 Publication Date:
 Grant/Contract Number:
 FG0211ER16211; SC0006028; FG0212ER46875
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of Chemical Physics
 Additional Journal Information:
 Journal Volume: 147; Journal Issue: 4; Journal ID: ISSN 00219606
 Publisher:
 American Institute of Physics (AIP)
 Research Org:
 Univ. of Illinois, UrbanaChampaign, IL (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC22); National Science Foundation (NSF); CREST, Japan Science and Technology Agency
 Country of Publication:
 United States
 Language:
 English
 Subject:
 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
 OSTI Identifier:
 1473852
 Alternate Identifier(s):
 OSTI ID: 1372946
Hirata, So, Doran, Alexander E., Knowles, Peter J., and Ortiz, J. V.. Oneparticle manybody Green’s function theory: Algebraic recursive definitions, linkeddiagram theorem, irreduciblediagram theorem, and generalorder algorithms. United States: N. p.,
Web. doi:10.1063/1.4994837.
Hirata, So, Doran, Alexander E., Knowles, Peter J., & Ortiz, J. V.. Oneparticle manybody Green’s function theory: Algebraic recursive definitions, linkeddiagram theorem, irreduciblediagram theorem, and generalorder algorithms. United States. doi:10.1063/1.4994837.
Hirata, So, Doran, Alexander E., Knowles, Peter J., and Ortiz, J. V.. 2017.
"Oneparticle manybody Green’s function theory: Algebraic recursive definitions, linkeddiagram theorem, irreduciblediagram theorem, and generalorder algorithms". United States.
doi:10.1063/1.4994837. https://www.osti.gov/servlets/purl/1473852.
@article{osti_1473852,
title = {Oneparticle manybody Green’s function theory: Algebraic recursive definitions, linkeddiagram theorem, irreduciblediagram theorem, and generalorder algorithms},
author = {Hirata, So and Doran, Alexander E. and Knowles, Peter J. and Ortiz, J. V.},
abstractNote = {A thorough analytical and numerical characterization of the whole perturbation series of oneparticle manybody Green’s function (MBGF) theory is presented in a pedagogical manner. Three distinct but equivalent algebraic (firstquantized) recursive definitions of the perturbation series of the Green’s function are derived, which can be combined with the wellknown recursion for the selfenergy. Six generalorder 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 perturbationscaled Hamiltonian. They all display the identical, nondivergent perturbation series except ΔMPn, which agrees with MBGF in the diagonal and frequencyindependent approximations at 1 ≤ n ≤ 3 but converges at the fullconfigurationinteraction (FCI) limit at n=∞ (unless it diverges). Numerical data of the perturbation series are presented for Koopmans and nonKoopmans states to quantify the rate of convergence towards the FCI limit and the impact of the diagonal, frequencyindependent, or ΔMPn approximation. The diagrammatic linkedness and thus sizeconsistency of the oneparticle Green’s function and selfenergy are demonstrated at any perturbation order on the basis of the algebraic recursions in an entirely timeindependent (frequencydomain) framework. The trimming of external lines in a oneparticle Green’s function to expose a selfenergy 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 frequencyindependent approximations at 1 ≤ n ≤ 3 is algebraically proven, also ascribing the differences at n = 4 to the socalled semireducible and linkeddisconnected diagrams},
doi = {10.1063/1.4994837},
journal = {Journal of Chemical Physics},
number = 4,
volume = 147,
place = {United States},
year = {2017},
month = {7}
}