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arXiv:cond-mat/9301024

Anyons as Dirac Strings the $A_x=0$ Gauge

McCabe, John

Published Jan 20, 1993• 0 citations
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Abstract

We show how to quantize the anyon particle theory in the gauge $A_x=0$, where the statistical potential $\vec A(\vec x)$ is a Dirac string. In this gauge, anyons obey normal statistics.

DOI
10.48550/arxiv.cond-mat/9301024

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Anyons as Dirac Strings the Ax=0A_x=0Ax​=0 Gauge
We show how to quantize the anyon particle theory in the gauge Ax=0A_x=0Ax​=0, where the statistical potential A⃗(x⃗)\vec A(\vec x)A(x) is a Dirac string. In this gauge, anyons obey normal statistics.
We construct a Hamiltonian for NNN anyons moving on the two-sphere. We show why the anyonic gauge coupling must satisfy a Dirac quantization condition, reproducing the braiding constraint on the statistical parameter. We then give a perturbative analysis of the NNN-body spectrum near Bose statistics.
We develop a density functional treatment of noninteracting Abelian anyons, which is capable, in principle, of dealing with a system of a large number of anyons in an external potential. Comparison with exact results for a few particles shows that the model captures the behavior qualitatively and semiquantitatively, especially in the vicinity of the fermionic statistics. We then study anyons with statistics parameter 1+1/n1+1/n1+1/n, which are thought to condense into a superconducting state. An indication of the superconducting behavior is the mean-field result that, for uniform density systems, the ground-state energy increases under the application of an external magnetic field independent of its direction. Our density functional theory based analysis does not find that to be the case for finite systems of anyons, which can accommodate a weak external magnetic field through density transfer between the bulk and the boundary rather than through transitions across effective Landau levels, but the ``Meissner repulsion'' of the external magnetic field is recovered in the thermodynamic limit as the effect of the boundary becomes negligible. We also consider the quantum Hall effect of anyons, and show that its topological properties, such as the charge and statistics of the excitations and the quantized Hall conductance, arise in a self-consistent fashion.