Statistics of skyrmions in Quantum Hall systems

TL;DR

This paper investigates the quantum statistical interactions of skyrmions in quantum Hall systems near specific filling fractions, revealing how their spin configurations influence their quantum statistics and resulting filling fractions.

Contribution

It introduces a Ginzburg-Landau framework to analyze skyrmion statistics and their role in determining fractional quantum Hall states based on skyrmion spin configurations.

Findings

Skyrmion exchange phases depend on spin and filling fraction.

Odd/even reversed spins lead to different quantum statistics.

Skyrmion condensation explains fractional filling fractions.

Abstract

We analyze statistical interactions of skyrmions in the quantum Hall system near a critical filling fraction in the framework of the Ginzburg-Landau model. The phase picked up by the wave-function during an exchange of two skyrmions close to $\nu=1/(2n+1)$ is $\pi[S+1/2(2n+1)]$, where $S$ is the skyrmion's spin. In the same setting an exchange of two fully polarized vortices gives rise to the phase $\pi/(2n+1)$. Skyrmions with odd and even numbers of reversed spins have different quantum statistics. Condensation of skyrmions with an even number of reversed spins leads to filling fractions with odd denominators, while condensation of those with an odd number of reversed spins gives rise to filling fractions with even denominators.