Comparison of methods for computing the exchange energy in laterally coupled quantum dots

Details Comparison of methods for computing the exchange energy in laterally coupled quantum dots Comparison of methods for computing the exchange energy in laterally coupled quantum dots

2010-09-16

arxiv.org/abs/1009.3069v2

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

6 pages, 7 figures

Scientific paper

We calculate the exchange energy in two dimensional laterally coupled quantum dots using Heitler-London, Hund-Mullikan and variational methods. We assess the quality of these approximations in zero and finite magnetic fields comparing against numerically exact results. We find that over the much simpler Heitler-London method surprisingly, the Hund-Mullikan method does not offer any significant improvement, whether at large or small interdot distances. Contrary to that, our variational ansatz proves substantially better in a single dot at finite magnetic field, all approximate methods fail. This reflects the qualitative change of the single electron ground state from non-degenerate (harmonic oscillator) to highly degenerate (Landau level). However, we find that the magnetically induced failure does not occur in the most important, double-dot, regime.

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