Magnetic field dependence of the low-energy spectrum of a two-electron quantum dot

The low-energy eigenstates of two interacting electrons in a square quantum dot in a magnetic field are determined by numerical diagonalization. In th e strong correlation regime, the low-energy eigenstates show Aharonov-Bohm- type oscillations, which decrease in amplitude as the field increases. Thes e oscillations, including the decrease in amplitude, may be reproduced to g ood accuracy by an extended Hubbard model in a basis of localized one-elect ron Hartree states. The hopping matrix element t comprises the usual kineti c energy term plus a term derived from the Coulomb interaction. The latter is essential to get good agreement with exact results. The phase of t gives rise to the usual Peierls factor, related to the flux through a square def ined by the peaks of the Hartree wave functions. The magnitude of t decreas es slowly with magnetic field as the Hartree functions become more localize d, giving rise to the decreasing amplitude of the Aharonov-Bohm oscillation s.