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Modern Physics Letters A

GROUND STATE OF N HARMONICALLY BOUND ANYONS IN A MAGNETIC FIELD

R. Chitra

Published Dec 14, 1992• 0 citations
Publisher

Abstract

The properties of the ground state of N anyons in an external magnetic field and a harmonic oscillator potential are computed in the large-N limit using the Thomas-Fermi approximation. The number of level crossings in the ground state as a function of the harmonic frequency, the strength and the direction of the magnetic field and N are also studied.

DOI
10.1142/s0217732392003013

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The properties of the ground state of N anyons in an external magnetic field and a harmonic oscillator potential are computed in the large-N limit using the Thomas-Fermi approximation. The number of level crossings in the ground state as a function of the harmonic frequency, the strength and the direction of the magnetic field and N are also studied.
The complete set of ground state wave functions for N anyons in an external magnetic field on the torus is found. The cases when the filling factor is less than or equal to one are considered. The single valued description of anyons is employed throughout by coupling bosons to a Chern-Simons field. At the end, the Chern-Simons interaction is removed by a singular gauge transformation as a result of which the wave functions become multi-component in agreement with other studies. It is shown that for statistics of the type θ=πq/p the exactly filled lowest Landau level has a q-fold degeneracy. Statistics of type π/p, which are relevant for the Laughlin theory of the FQHE, are singled out as those with non-degenerate filled ground states.
The ground-state energy and wave function of many anyons in a harmonic oscillator potential is studied using perturbation theory from the fermionic and bosonic ends. As the number of anyons increases to infinity, the ground-state energy scales with the power 3/2. As the statistics parameter changes, there are repeated level crossings between states having different angular momenta. Hence the ground state is only piecewise continuous, and the number of pieces increases with the number of anyons. This is to be contrasted with the problem of interpolating statistics in one dimension where there are no level crossings in the ground state for any number of particles.
The mean field equations for anyons in an external homogeneous magnetic field are studied and two classes of mean field solutions are explicitly constructed. The first class of solutions, corresponding to one filled Landau level in the combined external and smeared out statistical magnetic fields, is compared to the corresponding exact groundstate solutions. The energies are found to agree well at low densities and when the statistical field is not too strong compared to the background field. At high densities the fermi pressure increases the mean field energy indefinitely. The mean field solutions also miss the lower part of the energy spectrum. To the second class of mean field solutions no corresponding anyon state is known. These solutions represent the anyonic continuation of the fermi state with two filled Landau levels.