Lower bounds on the exchange-correlation energy in reduced dimensions

Bounds on the exchange-correlation energy of many-electron systems are derived and tested. By using universal scaling properties of the electron-electron interaction, we obtain the exponent of the bounds in three, two, one, and quasione dimensions. From the properties of the electron gas in the dilu...

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Bibliographic Details
Published in:Physical review letters 2009-05, Vol.102 (20), p.206406-206406, Article 206406
Main Authors: Räsänen, E, Pittalis, S, Capelle, K, Proetto, C R
Format: Article
Language:English
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Summary:Bounds on the exchange-correlation energy of many-electron systems are derived and tested. By using universal scaling properties of the electron-electron interaction, we obtain the exponent of the bounds in three, two, one, and quasione dimensions. From the properties of the electron gas in the dilute regime, the tightest estimate to date is given for the numerical prefactor of the bound, which is crucial in practical applications. Numerical tests on various low-dimensional systems are in line with the bounds obtained and give evidence of an interesting dimensional crossover between two and one dimensions.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.102.206406