%0 Journal Article
%A Creffield, Charles
%A Jefferson, John H
%A Sarkar,, Sarben
%A Tipton, D. L. J.
%T Magnetic field dependence of the low-energy spectrum of a two-electron quantum dot
%D 2000
%@ 1098-0121
%U https://hdl.handle.net/20.500.14352/59753
%X 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 wave functions. 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.
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