# Kohn-Sham Theory of the Fractional Quantum Hall Effect

## TL;DR

This paper develops a Kohn-Sham density functional theory framework for the fractional quantum Hall effect by mapping electrons to composite fermions, capturing topological properties and enabling realistic modeling of various physical phenomena.

## Contribution

It introduces a novel Kohn-Sham approach for the fractional quantum Hall effect using composite fermions, allowing for detailed and realistic simulations of topological and edge properties.

## Key findings

- Captures fractional charge and braid statistics
- Models non-uniform density configurations
- Enables simulation of edge and disorder effects

## Abstract

We formulate the Kohn-Sham equations for the fractional quantum Hall effect by mapping the original electron problem into an auxiliary problem of composite fermions that experience a density dependent effective magnetic field. Self-consistent solutions of the KS equations demonstrate that our formulation captures not only configurations with non-uniform densities but also topological properties such as fractional charge and fractional braid statistics for the quasiparticles excitations. This method should enable a realistic modeling of the edge structure, the effect of disorder, spin physics, screening, and of fractional quantum Hall effect in mesoscopic devices.