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arXiv:cond-mat/9906052 · Physics Letters A

Universal correlations of one-dimensional interacting electrons in the gas phase

F. Göhmann, V. E. Korepin

Published Sep 1, 1999• 11 citations
arXivHTMLPDF
DOI
10.1016/s0375-9601(99)00587-3

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Similar to the bosonization method in one dimension, we divide the electron operators in phase space into two component operators, and study three-dimensional homogeneous electron gas with a strong correlation effect. We apply this method to calculate the pair distribution function g(r = 0, r s ) and the renormalization coefficient of the one-electron Green's function Z(k F ) (Z F ), and show that it has great advantages of succinctness and efficiency for studying one- and three-dimensional systems with a strong correlation effect. This method can be applied to investigate interaction quenches in ultracold atomic gases.
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.