Ground State Energy of Fractionally Charged Quasiparticles

Considering two dimensional (2-D) electron gas as one component plasma (OCP), for the state at the Landau level filling factor 1/3, Laughlin has found a many body wave function with a lower energy than the single particle energy. We plot the ground state energy of this wave function versus different m (angular momentum) by using the modified hypernetted chain technique. Comparing the plot with the one that we have from the charge density wave (CDW), we see that for small m the energy of Laughlin’s state is more negative than that of CDW. But the energy differences are smaller at higher m and hence the fractions become weaker along the series 1/3, 1/5, 1/7.... We obtain the ground state energy for many different fractions of charges. Also we report our calculation of the variation of states in terms of magnetic field.