Creffield, CharlesJefferson, John HSarkar,, SarbenTipton, D. L. J.2023-06-202023-06-202000-09-151098-012110.1103/PhysRevB.62.7249https://hdl.handle.net/20.500.14352/59753© 2000 The American Physical Society. The authors would like to thank Wolfgang Häusler and Colin Lambert for stimulating discussions. C.E.C. acknowledges support from the Leverhulme Foundation and from the EV within the TMR programme. Support from the U.K. Ministry of Defense and the E.U. TMR program is also acknowledged.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.engjournal articlehttp://dx.doi.org/10.1103/PhysRevB.62.7249http://journals.aps.orgopen access538.9Interacting electronsFísica de materialesFísica del estado sólido2211 Física del Estado Sólido