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Acta Physica Sinica

AN ALTERNATE PROOF OF THE INFINITE ORDER PERTURBATION THEORY BY MATRIX PARTITION

ZHENG ZHAO-BO, 中国科学技术大学物理系

Published Jan 1, 1981• 1 citation
Publisher

Abstract

Recently, Wu and his coworkers formulated an infinite order perturbation theory for solving the Green's function of a disordered system, using a diagrammatic technique. In this paper, the method of matrix partition is used to obtain the same series of recursion relations, thus providing an algebraic proof for the theory.
DOI
10.7498/aps.30.866

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The second-order multireference perturbation theory employing multiple partitioning of the many-electron Hamiltonian into a zero-order part and a perturbation is formulated in terms of many-body diagrams. The essential difference from the standard diagrammatic technique of Hose and Kaldor concerns the rules of evaluation of energy denominators which take into account the dependence of the Hamiltonian partitioning on the bra and ket determinantal vectors of a given matrix element, as well as the presence of several two-particle terms in zero-order operators. The novel formulation naturally gives rise to a “sum-over-orbital” procedure of correlation calculations on molecular electronic states, particularly efficient in treating the problems with large number of correlated electrons and extensive one-electron bases. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 395–401, 1999
A new approach to the one-particle Green's functions G\mathit{G}G for finite electronic systems is presented. This approach is based on the diagrammatic perturbation expansions of the Green's function and of the dynamic self-energy part M\mathit{M}M related to G\mathit{G}G via the Dyson equation. The exact summation of the latter expansion is reformulated in terms of a simple algebraic form referred to as algebraic diagrammatic construction (ADC). The ADC defines in a systematical way a set of approximation schemes (nthn\mathrm{th}nth-order ADC schemes) that represent infinite partial summations for M\mathit{M}M and (via the Dyson equation) for G\mathit{G}G being complete through nthn\mathrm{th}nth order of perturbation theory. The corresponding mathematical procedures are essentially Hermitian eigenvalue problems in restricted configuration spaces of unperturbed ionic configurations. Explicit equations for the second-, third-, and fourth-order ADC schemes are derived and analyzed. While the second- and third-order schemes can be viewed as systematic rederivations of previous approximation schemes, the fourth-order ADC scheme represents a complete fourth-order approximation for the self-energy and the one-particle Green's function which was hitherto not available.