Interacting electrons and bosons in the doubly screened <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>G</mml:mi><mml:mover accent="true"><mml:mi>W</mml:mi><mml:mo></mml:mo></mml:mover></mml:mrow></mml:math> approximation: A time-linear scaling method for first-principles simulations
Y. Pavlyukh, Enrico Perfetto, Gianluca Stefanucci
Abstract
We augment the time-linear formulation of the Kadanoff-Baym equations for systems of interacting electrons and quantized phonons or photons with the $G\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{W}$ approximation, the Coulomb interaction $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{W}$ being dynamically screened by both electron-hole pairs and bosonic particles. We also show how to combine different approximations to include simultaneously multiple correlation effects in the dynamics. The final outcome is a versatile framework comprising ${2}^{12}$ distinct diagrammatic methods, each scaling linearly in time and preserving all fundamental conservation laws. The dramatic improvement over current state-of-the-art approximations brought about by $G\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{W}$ is demonstrated in a study of the correlation-induced charge migration of the glycine molecule in an optical cavity.