Abstract
We study ${N}_{e}$ interacting electrons confined in a one-dimensional quantum ring (QR) first by using a Hartree-Fock approximation and then by introducing correlation effects. An external magnetic field $B$ perpendicular to the ring plane is considered. The energy spectra of low-lying states of the QR as a function of $B$ and ${N}_{e}$ are obtained. A phase diagram is presented indicating a rich variety of ground states. By plotting the density functions of the QR, the ground-state configuration is found to be a regular polygon.
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