Charged and Neutral Vortex Excitations in a Mean Field Theory for the Fractional Quantum Hall Effect
Abstract
Applying a bi-local mean field approximation to the fractional quantum Hall state of =1/3, we obtain charged and neutral vortex mean field solutions numerically. We calculate the mean field energy and the fluctuation corrections. The charged vortex has a fractional charge and a fractional angular momentum. The neutral vortex is a bound state of two charged vortices and has a zero charge and a zero angular momentum. The creation energy of the neutral vortex is about a half of the pair creation energy of two charged vortices. The magnetic field dependence of the gap energy agrees with the Laughlin's quasiparticle gap energy.
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