The low-lying spectra of two-dimensional 3-electron and 4-electron narrow rings have been studied. It has been revealed that these spectra are simply dominated by a few favorable internal states. These internal states are free from the symmetry constraint and are nodeless in their wave functions (except the nodes when a pair of electrons overlap). The symmetry background of the fractional Aharonov-Bohm oscillation has been revealed. A very strong oscillation in the low-energy limit of the photon energy absorbed by the ground state against the magnetic field $B$ is found. The amplitude of oscillation is a few mega-electron-volts and is about ten times larger than the one of ground-state energy; the period is the same as the Aharonov-Bohm oscillation. The qualitative features found in this paper hold also for $N$-electron rings.

• Received 17 August 2005

DOI:https://doi.org/10.1103/PhysRevB.72.195310