Physical Review B - Condensed Matter and Materials Physics
Abstract
We introduce a supersymmetric Chern-Simons theory whose low energy physics is
that of the fractional quantum Hall effect. The supersymmetry allows us to
solve the theory analytically. We quantise the vortices and, by relating their
dynamics to a matrix model, show that their ground state wavefunction is in the
same universality class as the Laughlin state. We further construct coherent
state representations of the excitations of a finite number of vortices. These
are quasi-holes. By an explicit computation of the Berry phase, without
resorting to a plasma analogy, we show that these excitations have fractional
charge and spin.This is the author accepted manuscript. The final version is available from APS via http://dx.doi.org/10.1103/PhysRevB.92.23512