Finite-size studies of semion systems

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Abstract
The ground and the excited states of a two-dimensional anyon system are studied via finite-size numerical calculations in a spherical geometry. It is shown that Laughlin’s mean-field theory gives an accurate description of the ground-state properties of the finite, spherical system. We find, consistent with earlier analytic theories, that the collective mode of the system exhibits a linear dispersion in the long-wavelength limit, and predict a novel roton minimum at a finite value of the wave number q. We also discuss the consequences on the anyon spectrum of having a model repulsive interaction between the particles.