期刊
PHYSICAL CHEMISTRY CHEMICAL PHYSICS
卷 24, 期 16, 页码 9298-9307出版社
ROYAL SOC CHEMISTRY
DOI: 10.1039/d2cp00438k
关键词
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资金
- U.S. Department of Energy (Office of Basic Energy Sciences) [DE-SC0019215]
This study presents a geometric picture of electron-electron correlations using the dimensional scaling approach and quantifies correlations through entanglement. The results indicate the feasibility of using the geometrical picture to obtain an upper bound on electron-electron correlations at the large-D limit and at D = 3.
In electronic structure calculations, the correlation energy is defined as the difference between the mean field and the exact solution of the non relativistic Schrodinger 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 give a bound on the correlation energy. The results at the large-D limit and at D = 3 indicate the feasibility of using the geometrical picture to get a bound on the electron-electron correlations.
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