Abstract
We analyze singlet-triplet energy separation (exchange energy) in the double quantum dot system by performing the exact diagonalization of the two-electron Schr\"odinger equation. By projecting out the contributions from the various products of the single-particle states to the two-electron wave functions, we show that the admixture of the excited states gradually changes as the system exhibits a transition from the two strongly coupled dots with many states involved to two almost completely decoupled dots where contributions from only two lowest states are dominant. However, by comparing our numerically exact results with predictions of the Heitler-London approximation in the limit of the weak interdot coupling, we find that the quantum mechanical correlations between the different states remain non-negligible, even in this case, and lead to (1) the reduction of the magnetic field interval where the exchange energy is negative and (2) the faster overall decay of the exchange energy with increasing magnetic fields.
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