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

## TL;DR

This paper introduces an efficient tensor-contraction based method for computing the second-Born self-energy in nonequilibrium Green's function simulations, significantly improving computational speed for larger molecular systems.

## Contribution

The paper presents a novel tensor-contraction approach that accelerates second-Born self-energy calculations, enabling larger and more complex first-principles simulations.

## Key findings

- Achieved significant computational speed-up in molecular electron dynamics
- Demonstrated method's effectiveness on selected molecular systems
- Enhanced scalability of nonequilibrium Green's function simulations

## Abstract

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