Transition from vortex localization to electron localization in the fractional quantum Hall regime

Abstract

Using configuration-interaction calculations with optimized basis functions, the phase diagram of a quantum dot of ten electrons in the fractional quantum Hall regime has been obtained for magnetic fields up to filling factor $\ensuremath{\nu}=\frac{1}{3}$. The results for the ground state energy of the system show that a transition from a localized vortex distribution to a localized electron distribution occurs when the magnetic field passes through the value corresponding to $\ensuremath{\nu}=\frac{1}{2}$. The stability of the fractional quantum Hall phases in this finite system, depending on the stability of the vortex molecules at $\ensuremath{\nu}>\frac{1}{2}$ and the particle molecules at $\ensuremath{\nu}<\frac{1}{2}$, vanishes as the magnetic field approaches the value corresponding to $\ensuremath{\nu}=1∕2$.