Two electrons in a two-dimensional random potential: Exchange, interaction, and localization

The problem of two electrons in a two-dimensional random potential is addre ssed numerically. Specifically, the role of the Coulomb interaction between electrons on localization is investigated by writing the Hamiltonian on a localized basis and diagonalizing it exactly. The result of that procedure is discussed in terms of level statistics, the expectation value of the ele ctron-electron separation, and a configuration-space inverse participation number. We argue that, in the interacting problem, a localization-delocaliz ation crossover in real space does nor correspond exactly to a Poisson-Wign er crossover in level statistics.