Exact solution for two interacting electrons on artificial atoms and molecules in solids

We present a general scheme for finding the exact eigenstates of two electrons, with on-site repulsive potentials (Formula presented) on I impurities in a macroscopic crystal. The model describes impurities in doped semiconductors and artificial “molecules” in quantum dots. For quantum dots, the energy cost for adding two electrons is bounded by the single-electron spectrum, and does not diverge when (Formula presented) implying limitations on the validity of the Coulomb blockade picture. Analytic applications for (Formula presented) on a one-dimensional chain yield quantum delocalization and magnetic transitions.