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Complex time, shredded propagator method for large-scale GW calculations
Computational Physics · Submitted 18 Apr 2019
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The resulting cubic scaling GW method has a sufficiently small prefactor to outperform standard quartic scaling methods on small systems ($\gtrapprox$ 10 atoms) and also represents a substantial improvement over other cubic methods tested for all system sizes studied.
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The abstract, sentence by sentence
The GW method is a many-body electronic structure technique capable of generating accurate quasiparticle properties for realistic systems spanning physics, chemistry, and materials science. Despite its power, GW is not routinely applied to large complex assemblies due to its large computational overhead and quartic scaling with particle number. Here, the GW equations are recast, exactly, as Fourier-Laplace time integrals over complex time propagators. The propagators are then "shredded" via energy partitioning and the time integrals approximated in a controlled manner using generalized Gaussian quadrature(s) while discrete variable methods are employed to represent the required propagators in real-space. The resulting cubic scaling GW method has a sufficiently small prefactor to outperform standard quartic scaling methods on small systems ($\gtrapprox$ 10 atoms) and also represents a substantial improvement over other cubic methods tested for all system sizes studied. The approach can be applied to any theoretical framework containing large sums of terms with energy differences in the denominator.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The GW method is a many-body electronic structure technique capable of generating accurate quasiparticle properties for realistic systems spanning physics, chemistry, and materials science. | background 1.00 | 0.05 | 0.03 | asserted 1.00 |
| s1 | Despite its power, GW is not routinely applied to large complex assemblies due to its large computational overhead and quartic scaling with particle number. | background 0.67 | 0.07 | 0.03 | asserted 1.00 |
| s2 | Here, the GW equations are recast, exactly, as Fourier-Laplace time integrals over complex time propagators. | method 0.61 | 0.92 | 0.08 | asserted 1.00 |
| s3 | The propagators are then "shredded" via energy partitioning and the time integrals approximated in a controlled manner using generalized Gaussian quadrature(s) while discrete variable methods are employed to represent the required propagators in real-space. | method 0.99 | 0.91 | 0.07 | asserted 1.00 |
| s4 | The resulting cubic scaling GW method has a sufficiently small prefactor to outperform standard quartic scaling methods on small systems ($\gtrapprox$ 10 atoms) and also represents a substantial improvement over other cubic methods tested for all system sizes studied. | result 0.97 | 0.91 | 0.75 | asserted 0.99 |
| s5 | The approach can be applied to any theoretical framework containing large sums of terms with energy differences in the denominator. | interpretation 0.86 | 0.38 | 0.07 | asserted 0.74 |
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Original abstract
The GW method is a many-body electronic structure technique capable of generating accurate quasiparticle properties for realistic systems spanning physics, chemistry, and materials science. Despite its power, GW is not routinely applied to large complex assemblies due to its large computational overhead and quartic scaling with particle number. Here, the GW equations are recast, exactly, as Fourier-Laplace time integrals over complex time propagators. The propagators are then "shredded" via energy partitioning and the time integrals approximated in a controlled manner using generalized Gaussian quadrature(s) while discrete variable methods are employed to represent the required propagators in real-space. The resulting cubic scaling GW method has a sufficiently small prefactor to outperform standard quartic scaling methods on small systems ($\gtrapprox$ 10 atoms) and also represents a substantial improvement over other cubic methods tested for all system sizes studied. The approach can be applied to any theoretical framework containing large sums of terms with energy differences in the denominator.
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