Influence of variations in the electron–electron interaction on the ground state metric space “band structure” of a two-electron magnetic system

• We study the unique relationship of CDFT for a model system using metric spaces.
• Varying the strength of the inter-electron interaction generates a “band structure”.
• The “band structure” exhibits “bands” and “gaps” for all metric spaces considered.
• The characteristics are similar to those found by varying the confinement potential.

We consider a model system of two electrons confined in a two-dimensional harmonic oscillator potential, with the electrons interacting via an α/r2α/r2 potential, and subject to a magnetic field applied perpendicular to the plane of confinement. Our results show that variations in the strength of the electron–electron interaction generate a “band structure” in ground state metric spaces, which shares many characteristics with those generated as a result of varying the confinement potential. In particular, the metric spaces for wavefunctions, particle densities, and paramagnetic current densities all exhibit distinct “bands” and “gaps”. The behavior of the polar angle of the bands also shares traits with that obtained by varying the confinement potential, but the behavior of the arc lengths of the bands on the metric space spheres can be seen to be different for the two cases and opposite for a large range of angular momentum values. The findings here and in Refs. [1] and [2] demonstrate that the “band structure” that arises in ground state metric spaces when a magnetic field is applied is a robust feature.