Interacting electrons in polygonal quantum dots

The low-lying eigenstates of a system of two electrons confined within a tw o-dimensional quantum dot with a hard polygonal boundary are obtained by me ans of exact diagonalization. The transition from a weakly correlated charg e distribution for small dots to a strongly correlated "Wigner molecule" fo r large dots is studied, and the behavior at the crossover is determined. I n sufficiently large dots, a recently proposed mapping to an effective char ge-spin model is investigated, and is found to produce the correct ordering of the energy levels and to give a good first approximation to the size of the level spacings. We conclude that this approach is a valuable method to obtain the low-energy spectrum of few-electron quantum dots. [S0163-1829(9 9)03715-7].