Linear Scaling

This page gathers publications focused on scalable computational methods for atomistic many-body calculations, especially Coulomb and exchange matrix elements and large-scale excitonic simulations.

Exploiting underlying crystal lattice for efficient computation of Coulomb matrix elements in multi-million atoms nanostructures

Phys. Rev. B 9, 4 (2023)

This work presents an updated strategy for computing Coulomb matrix elements directly on a regular grid superimposed on the underlying crystal lattice. It removes the need for an auxiliary basis transfer while retaining near-linear practical scaling.

Keywords: Coulomb integrals, linear scaling

Main result: Coulomb matrix elements for multi-million-atom systems can be computed with O(N log N) scaling while remaining numerically consistent with direct summation. This substantially expands the feasible size of atomistic many-body calculations.

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Efficient computation of Coulomb and exchange integrals for multi-million atom nanostructures

Comput. Phys. Commun. 238, 254–261 (2019)

This work develops a practical route to compute Coulomb and exchange integrals for atomistic nanostructures containing millions of atoms. It addresses a central computational bottleneck of configuration-interaction calculations at realistic system sizes.

Keywords: Coulomb integrals, linear scaling

Main result: Coulomb and exchange integrals for very large atomistic nanostructures can be computed efficiently enough for realistic many-body studies. The method turns previously prohibitive calculations into practical simulations.

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Linear scaling approach for atomistic calculation of excitonic properties of 10-million-atom nanostructures

Phys. Rev. B 94, 045440 (2016)

This work pushes atomistic excitonic calculations toward the 10-million-atom scale using scalable numerical strategies. It demonstrates that excitonic properties of truly large nanostructures can be treated without abandoning atomistic resolution.

Keywords: linear scaling

Main result: excitonic calculations at the 10-million-atom scale become computationally feasible with a linear-scaling atomistic framework. This opens realistic many-body modeling for structures far beyond traditional limits.

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