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Homogeneous electron gas in arbitrary dimensions

R. Schlesier, C. Benavides-Riveros, M. Marques

Physical Review B, 102, 035123, (2020)

DOI: 10.1103/physrevb.102.035123

Download: BibTEX

The homogeneous electron gas is one of the most studied model systems in condensed-matter physics. It is also the basis of the large majority of approximations to the functionals of density-functional theory. As such, its exchange-correlation energy has been studied extensively, and it is well-known for systems of one, two, and three 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 like a polynomial: −cD/rγDs, with the exponent γD=(D−3)/(D−1). In the large-D limit, the value of cD is found to depend linearly on the dimension. In this limit, we also find that the concepts of exchange and correlation merge, sharing a common 1/rs dependence.

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{"type":"article", "name":"r.schlesier20207", "author":"R. Schlesier and C. Benavides-Riveros and M. Marques", "title":"Homogeneous electron gas in arbitrary dimensions", "journal":"Physical Review B", "volume":"102", "OPTnumber":"3", "OPTmonth":"7", "year":"2020", "OPTpages":"035123", "OPTnote":"", "OPTkey":"", "DOI":"10.1103/physrevb.102.035123"}
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