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Cubic-scaling iterative solution of the Bethe-Salpeter equation for finite systems

hal.structure.identifierDonostia International Physics Center [DIPC]
hal.structure.identifierDepartment of Physics [Marburg]
dc.contributor.authorLJUNGBERG, Mathias P.
hal.structure.identifierDonostia International Physics Center [DIPC]
dc.contributor.authorKOVAL, Peter
hal.structure.identifierDipartimento di Scienza dei Materiali
hal.structure.identifierDonostia International Physics Center [DIPC]
dc.contributor.authorFERRARI, Francesco
hal.structure.identifierLaboratoire Ondes et Matière d'Aquitaine [LOMA]
dc.contributor.authorFOERSTER, Dietrich
hal.structure.identifierCentro de Fisica de Materiales [CFM]
hal.structure.identifierDonostia International Physics Center [DIPC]
dc.contributor.authorSANCHEZ-PORTAL, Daniel
dc.date.created2015-05-20
dc.date.issued2015-08-17
dc.identifier.issn1098-0121
dc.description.abstractEnThe 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
dc.description.sponsorshipPrédiction par calcul numérique intensif du potentiel à circuit ouvert au sein de cellules photovoltaïques organiques. - ANR-12-MONU-0014
dc.language.isoen
dc.publisherAmerican Physical Society
dc.subject.enExcited states: methodology
dc.subject.enMolecular spectra
dc.subject.enStrongly correlated electron systems: generalized tight-binding method
dc.title.enCubic-scaling iterative solution of the Bethe-Salpeter equation for finite systems
dc.typeArticle de revue
dc.identifier.doi10.1103/PhysRevB.92.075422
dc.subject.halPhysique [physics]/Matière Condensée [cond-mat]/Science des matériaux [cond-mat.mtrl-sci]
dc.identifier.arxiv1505.05440
bordeaux.journalPhysical Review B: Condensed Matter and Materials Physics (1998-2015)
bordeaux.page075422 (1-18)
bordeaux.volume92
bordeaux.issue7
bordeaux.peerReviewedoui
hal.identifierhal-01192976
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01192976v1
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