Singlet-triplet splitting, correlation and entanglement of two electrons in quantum dot molecules

TL;DR

This paper investigates the electronic properties of two-electron quantum dot molecules using advanced pseudopotential and configuration-interaction methods, highlighting the limitations of simpler models in accurately capturing entanglement and correlation effects.

Contribution

It provides a detailed comparison of various approximation methods against accurate calculations, revealing their strengths and weaknesses in modeling quantum dot molecules.

Findings

Hartree-Fock and local spin density fail to accurately predict singlet-triplet splitting and entanglement.

Hubbard model captures ground state symmetry but misestimates entanglement due to strain effects.

Heisenberg model is accurate only at large inter-dot separations, overestimating entanglement.

Abstract

Starting with an accurate pseudopotential description of the single-particle states, and following by configuration-interaction treatment of correlated electrons in vertically coupled, self-assembled InAs/GaAs quantum dot-molecules, we show how simpler, popularly-practiced approximations, depict the basic physical characteristics including the singlet-triplet splitting, degree of entanglement (DOE) and correlation. The mean-field-like single-configuration approaches such as Hartree-Fock and local spin density, lacking correlation, incorrectly identify the ground state symmetry and give inaccurate values for the singlet-triplet splitting and the DOE. The Hubbard model gives qualitatively correct results for the ground state symmetry and singlet-triplet splitting, but produces significant errors in the DOE because it ignores the fact that the strain is asymmetric even if the dots within a molecule are identical. Finally, the Heisenberg model gives qualitatively correct ground state symmetry and singlet-triplet splitting only for rather large inter-dot separations, but it greatly overestimates the DOE as a consequence of ignoring the electron double occupancy effect.