Interacting electrons in a magnetic field in a center-of-mass free basis

TL;DR

This paper extends a configuration-interaction method for four electrons in a quantum dot, using group theory and coordinate transformations to improve accuracy and reduce computational basis size.

Contribution

It introduces a group-theoretical basis decomposition that explicitly separates center-of-mass motion, enhancing the efficiency and precision of electron interaction calculations.

Findings

Significant reduction in basis set size.

Improved accuracy over standard methods.

Explicit identification of spurious center-of-mass states.

Abstract

We present an extension of the spin-adapted configuration-interaction method for the computation of four electrons in a quasi two-dimensional quantum dot. By a group-theoretical decomposition of the basis set and working with relative and center-of-mass coordinates we obtain an analytical identification of all spurious center-of-mass states of the Coulomb-interacting electrons. We find a substantial reduction in the basis set used for numerical computations. At the same time we increase the accuracy compared to the standard spin-adapted configuration-interaction method (SACI) due to the absence of distortions caused by an unbalanced cut-off of center-of-mass excitations.