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- W1531036014 abstract "The model N-fermion system studied in two previous papers is reconsidered in order to investigate the range of validity of diagrammatic many-body perturbation theory and various selective summations of higher order graphs. The familiar random phase approximation or bubble graph sum is shown to be the first term in an expansion in powers of 1/N for which the coefficients are arbitrary functions of NV/ε, where V is the interaction strength and ε is the level separation of the non-interacting system. However, the 1/N expansion converges very slowly (if at all) for N < 40. Other corrections to the bubble sum which do not fit into such an expansion are shown to be much more important than the 1/N corrections for small N. These are the exchange and self-energy graphs which correct for counting errors and violations of the exclusion principle when enumerating the states that a given particle can occupy. With these terms a rather good approximation to the excitation energy can be obtained, though the results are not quite as good as that obtained with fourth-order perturbation theory for small N, or for the whole range of N with the self-consistent linearization procedure described in a previous paper." @default.
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- W1531036014 date "1965-02-01" @default.
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- W1531036014 title "Validity of many-body approximation methods for a solvable model" @default.
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- W1531036014 doi "https://doi.org/10.1016/0029-5582(65)90864-3" @default.
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