Cubic-scaling iterative solution of the Bethe-Salpeter equation for finite systems Article Swipe
Mathias P. Ljungberg
,
Peter Koval
,
Francesco Ferrari
,
D. Foerster
,
Daniel Sánchez‐Portal
·
YOU?
·
· 2015
· Open Access
·
· DOI: https://doi.org/10.1103/physrevb.92.075422
YOU?
·
· 2015
· Open Access
·
· DOI: https://doi.org/10.1103/physrevb.92.075422
The Bethe-Salpeter equation (BSE) is currently the state of the art in the description of neutral electron excitations in both solids and large finite systems. It is capable of accurately treating charge-transfer excitations that present difficulties for simpler approaches. We present a local basis set formulation of the BSE for molecules where the optical spectrum is computed with the iterative Haydock recursion scheme, leading to a low computational complexity and memory footprint. Using a variant of the algorithm we can go beyond the Tamm-Dancoff approximation (TDA). We rederive the recursion relations for general matrix elements of a resolvent, show how they translate into continued fractions, and study the convergence of the method with the number of recursion coefficients and the role of different terminators. Due to the locality of the basis functions the computational cost of each iteration scales asymptotically as $O(N^3)$ with the number of atoms, while the number of iterations is typically much lower than the size of the underlying electron-hole basis. In practice we see that , even for systems with thousands of orbitals, the runtime will be dominated by the $O(N^2)$ operation of applying the Coulomb kernel in the atomic orbital representation
Related Topics
Concepts
Basis (linear algebra)
Recursion (computer science)
Convergence (economics)
Basis function
Coulomb
Kernel (algebra)
Scaling
Matrix (chemical analysis)
Physics
Applied mathematics
Statistical physics
Quantum mechanics
Mathematics
Electron
Algorithm
Discrete mathematics
Materials science
Composite material
Economic growth
Economics
Geometry
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1103/physrevb.92.075422
- OA Status
- green
- Cited By
- 41
- References
- 78
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W1779844773
All OpenAlex metadata
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https://openalex.org/W1779844773Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.1103/physrevb.92.075422Digital Object Identifier
- Title
-
Cubic-scaling iterative solution of the Bethe-Salpeter equation for finite systemsWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
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2015Year of publication
- Publication date
-
2015-08-17Full publication date if available
- Authors
-
Mathias P. Ljungberg, Peter Koval, Francesco Ferrari, D. Foerster, Daniel Sánchez‐PortalList of authors in order
- Landing page
-
https://doi.org/10.1103/physrevb.92.075422Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/1505.05440Direct OA link when available
- Concepts
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Basis (linear algebra), Recursion (computer science), Convergence (economics), Basis function, Coulomb, Kernel (algebra), Scaling, Matrix (chemical analysis), Physics, Applied mathematics, Statistical physics, Quantum mechanics, Mathematics, Electron, Algorithm, Discrete mathematics, Materials science, Composite material, Economic growth, Economics, GeometryTop concepts (fields/topics) attached by OpenAlex
- Cited by
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41Total citation count in OpenAlex
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2025: 2, 2024: 2, 2023: 5, 2022: 3, 2021: 1Per-year citation counts (last 5 years)
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78Number of works referenced by this work
- Related works (count)
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10Other works algorithmically related by OpenAlex
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