Invariance of the correlation energy at high density and large dimension in two-electron systems

Details Invariance of the correlation energy at high density and large dimension in two-electron systems Invariance of the correlation energy at high density and large dimension in two-electron systems

2010-05-05

arxiv.org/abs/1005.0676v5

Phys. Rev. Lett. 105, 113001 (2010)

Physics

Condensed Matter

Strongly Correlated Electrons

4 pages, 1 figure, to appear in Phys. Rev. Lett

Scientific paper

10.1103/PhysRevLett.105.113001

We prove that, in the large-dimension limit, the high-density correlation energy $\Ec$ of two opposite-spin electrons confined in a $D$-dimensional space and interacting {\em via} a Coulomb potential is given by $\Ec \sim -1/(8D^2)$ for any radial confining potential $V(r)$. This result explains the observed similarity of $\Ec$ in a variety of two-electron systems in three-dimensional space.

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