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Modern Physics Letters B

MEAN-FIELD THEORY OF ANYONS NEAR BOSE STATISTICS

JOHN MCCABE, R. MacKenzie

Published Jan 10, 1994• 0 citations
Publisher

Abstract

We argue the validity of a mean-field approximation for a free anyon gas near Bose statistics, and show that the anyon gas can exhibit a Meissner effect in the domain of validity of the approximation only due to a hard-core repulsion.
DOI
10.1142/s0217984994000054

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We examine an approach to justifying the mean field approximation for the anyon gas, using the scattering of anyons. Parity violation permits a nonzero average scattering angle, from which one can extract a mean radius of curvature for anyons. If this is larger than the interparticle separation, one expects that the graininess of the statistical magnetic field is unimportant, and that the mean field approximation is good. We argue that a non-conventional interaction between anyons is crucial, in which case the criterion for validity of the approximation is identical to the one deduced using a self-consistency argument.
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We study the physics of the mean field ansatz in a simplified anyon model. The model is solved exactly in a finite geometry with particular attention to boundary conditions compatible with a mean statistical magnetic field. The spectrum consists of bosonic plasma-like density fluctuations with a gap. We find that the repulsive Coulomb interactions introduced by the fluctuations around the mean field force the statistical charge and magnetic field to become localized near the boundaries. Translational invariance, broken by the mean field, is restored in the infinite volume limit as the statistical charge and magnetic field escape to infinity. The polarization effects of an external magnetic field and the role of “large” gauge transformations are also studied.