  The low-energy eigenstates of two interacting electrons in a square quantum
dot in a magnetic field are determined by numerical diagonalization. In the
strong correlation regime, the low-energy eigenstates show Aharonov-Bohm type
oscillations, which decrease in amplitude as the field increases. These
oscillations, including the decrease in amplitude, may be reproduced to good
accuracy by an extended Hubbard model in a basis of localized one-electron
Hartree states. The hopping matrix element, $t$, comprises the usual kinetic
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 defined by
the peaks of the Hartree wavefunctions. The magnitude of $t$ decreases slowly
with magnetic field as the Hartree functions become more localized, giving rise
to the decreasing amplitude of the Aharonov-Bohm oscillations.
