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 U_i, 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 U_i approaches infinity, implying limitations on the validity of the Coulomb blockade picture. Analytic applications on a one-dimensional chain yield quantum delocalization and magnetic transitions.