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Homogeneous electron gas in arbitrary dimensions

Authors: R. Schlesier, C.L. Benavides-Riveros, and M.A.L. Marques

Ref.: Phys. Rev. B 102, 035123 (2020)

Abstract: The homogeneous electron gas is one of the most studied model systems in condensed matter physics. It is also at the basis of the large majority of approximations to the functionals of density functional theory. As such, its exchange-correlation energy has been extensively studied, and is well-known for systems of 1, 2, and 3 dimensions. Here, we extend this model and compute the exchange and correlation energy, as a function of the Wigner-Seitz radius rs, for arbitrary dimension D. We find a very different behavior for reduced dimensional spaces (D = 1 and 2), our three dimensional space, and for higher dimensions. In fact, for D > 3, the leading term of the correlation energy does not depend on the logarithm of rs (as for D = 3), but instead scales polynomialy: -cD/rsγD,with the exponent γD = (D-3)/(D-1). In the large-D limit, the value of cD is found to depend linearly with the dimension. In this limit, we also find that the concepts of exchange and correlation merge, sharing a common 1/rs dependence.

Citations: 0 (Google scholar)

DOI: 10.1103/PhysRevB.102.035123

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Bibtex:

@article{Schlesier_2020,
	doi = {10.1103/physrevb.102.035123},
	url = {https://doi.org/10.1103%2Fphysrevb.102.035123},
	year = 2020,
	month = {jul},
	publisher = {American Physical Society ({APS})},
	volume = {102},
	number = {3},
	author = {Robert Schlesier and Carlos L. Benavides-Riveros and Miguel A. L. Marques},
	title = {Homogeneous electron gas in arbitrary dimensions},
	journal = {Physical Review B}
}