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Geometrical picture of the electron-electron correlation at the large-D limit by Ghosh, Kumar J. B.; Kais, Sabre; Herschbach, Dudley R. is a scholarly article available to read on EtoBox.

What is Geometrical picture of the electron-electron correlation at the large-D limit about?

In electronic structure calculations, the correlation energy is defined as the difference between the mean field and the exact solution of the non relativistic Schr\"odinger equation. Such an error in the different calculations is not directly observable as there is no simple quantum mechanical operator, apart from correlation functions, that correspond to such quantity. Here, we use the dimensional scaling approach, in which the electrons are localized at the large-dimensional scaled space, to describe a geometric picture of the electronic correlation. Both, the mean field, and the exact solutions at the large-D limit have distinct geometries. Thus, the difference might be used to describe the correlation effect. Moreover, correlations can be also described and quantified by the entanglement between the electrons, which is a strong correlation without a classical analog. Entanglement is directly observable and it is one of the most striking properties of quantum mechanics and bounded by the area law for local gapped Hamiltonians of interacting many-body systems. This study opens up the possibility of presenting a geometrical picture of the electron-electron correlations and might

Author

Ghosh, Kumar J. B.; Kais, Sabre; Herschbach, Dudley R.

Published

2021

Language

EN