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 $1/{N}^{3}$ while the second-order MBPT contribution to the band energy converges as $1/{N}^{2}$ . These convergence behaviors are demonstrated numerically for polyacetylene.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 $1/{N}^{3}$ while the second-order MBPT contribution to the band energy converges as $1/{N}^{2}$. These convergence behaviors are demonstrated numerically for polyacetylene.

Physical Review LettersJan 12, 199822 citations

N

1/{N}^{3}

while the second-order MBPT contribution to the band energy converges as

1/{N}^{2}

. These convergence behaviors are demonstrated numerically for polyacetylene.