Dimensionality dependence of the self-interaction correction in the local-density approximation to density functional theory

The local-density approximation (LDA) to density functional theory is not self-interaction free. Motivated by this intellectual challenge, and the possible practical importance of strong electron-correlation in a Wigner-type model, the capability of LDA is investigated for a two-dimensional electron system in the low-density limit. It is found for this essentially single-electron limit that the performance of LDA is slightly better in two dimension than in the equivalent three-dimensional problem treated earlier in Phys. Rev. B 18, 6506 (1978). An a priori explanation of this fact is given in terms of the different characters of potential fields generated by normalized charge distributions in these dimensions.