Kohn-Sham Density Functional Theory of Abelian Anyons

TL;DR

This paper develops a density functional theory for abelian anyons, capturing their behavior and topological properties, and explores their potential for superconductivity and quantum Hall effects.

Contribution

It introduces a density functional approach for large systems of abelian anyons, including analysis of superconducting and quantum Hall phenomena, with comparisons to exact results.

Findings

Qualitative and semi-quantitative agreement with exact few-particle results.

Indications of superconducting behavior in certain anyon systems.

Topological properties of quantum Hall states emerge self-consistently.

Abstract

We develop a density functional treatment of non-interacting 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 few particles shows that the model captures the behavior qualitatively and semi-quantitatively, especially in the vicinity of the fermionic statistics. We then study anyons with statistics parameter $1+1/n$, 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.