English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In electronic structure calculations, the correlation energy is defined asthe difference between the mean field and the exact solution of the nonrelativistic Schr\"odinger equation. Such an error in the differentcalculations is not directly observable as there is no simple quantummechanical operator, apart from correlation functions, that correspond to suchquantity. Here, we use the dimensional scaling approach, in which the electronsare localized at the large-dimensional scaled space, to describe a geometricpicture of the electronic correlation. Both, the mean field, and the exactsolutions at the large-D limit have distinct geometries. Thus, the differencemight be used to describe the correlation effect. Moreover, correlations can bealso described and quantified by the entanglement between the electrons, whichis a strong correlation without a classical analog. Entanglement is directlyobservable and it is one of the most striking properties of quantum mechanicsand bounded by the area law for local gapped Hamiltonians of interactingmany-body systems. This study opens up the possibility of presenting ageometrical picture of the electron-electron correlations and might give abound on the correlation energy. The results at the large-D limit and at D=3indicate the feasibility of using the geometrical picture to get a bound on theelectron-electron correlations.

Geometrical picture of the electron-electron correlation at the large-D limit