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In the nonequilibrium Green's function approach, the approximation of thecorrelation self-energy at the second-Born level is of particular interest,since it allows for a maximal speed-up in computational scaling when usedtogether with the Generalized Kadanoff-Baym Ansatz for the Green's function.The present day numerical time-propagation algorithms for the Green's functionare able to tackle first principles simulations of atoms and molecules, butthey are limited to relatively small systems due to unfavourable scaling ofself-energy diagrams with respect to the basis size. We propose an efficientcomputation of the self-energy diagrams by using tensor-contraction operationsto transform the internal summations into functions of external low-levellinear algebra libraries. We discuss the achieved computational speed-up intransient electron dynamics in selected molecular systems.

Efficient computation of the second-Born self-energy using tensor-contraction operations