Alexander Odriazola, Ilja Makkonen, Mikko M. Ervasti, Alain Delgado, Augusto Gonzalez, Ari Harju
Extensive numerical calculations of the ground-state energy of charged 2D-quantum dots were performed by means of different theoretical and computational methods. Hartree-Fock, Configuration Interaction, Variational Monte Carlo and Density Functional Theory approaches were considered. On the basis of the numerical evidence, it was found that the correlation energies scale as E_{corr}/(\hbar\omega) \approx N^{3/4} f_{corr}(N^{1/4}\beta), where N is the number of electrons, the coupling constant \beta is the ratio between Coulomb and oscillator (\hbar\omega) characteristic energies, and f_{corr} is a universal function. An analytic expression for f_{corr} is provided based on a two-parameter fit. In addition, analytic expressions for the correlation energy per particle and for the fraction of the total energy associated to the correlation energy are also provided.
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http://arxiv.org/abs/1209.1408
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