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

TL;DR

This study compares various computational methods for calculating exchange energy in laterally coupled quantum dots, revealing the variational approach's superiority and the limitations of other methods under different magnetic field conditions.

Contribution

The paper provides a comprehensive comparison of Heitler-London, Hund-Mullikan, and variational methods, highlighting the variational method's improved accuracy for exchange energy calculations.

Findings

Hund-Mullikan method offers no significant improvement over Heitler-London.

Variational method significantly outperforms other methods.

Approximate methods fail in single-dot scenarios at finite magnetic fields.

Abstract

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 surprisingly, the Hund-Mullikan method does not offer any significant improvement over the much simpler Heitler-London method, 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.