The convergence behavior of many-body perturbation theory (MBPT) with lattice summations directly reflects the spatial property of electron correlation in extended systems. A knowledge of such properties is essential for both theory and numerical calculations. It is shown solely from theory that the second-order MBPT contribution to the total energy per unit cell in polymers converges with lattice size N as 1/N³ while the second-order MBPT contribution to the band energy converges as 1/N². These convergence behaviors are demonstrated numerically for polyacetylene.
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Sun et al. (1998) studied this question.
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