Multi-anyons in the magnetic field

TL;DR

This paper investigates how two types of anyons with fractional statistics respond to external magnetic fields, revealing different periodic behaviors in flux, with implications for understanding anyonic systems in two-dimensional geometries.

Contribution

It introduces a detailed analysis of two distinct anyon types under magnetic fields and explores their flux periodicities in complex geometries, highlighting novel behaviors.

Findings

Type I anyons have flux periodicity as an integer multiple of the flux quantum.

Type II anyons exhibit fractional flux periodicity.

The equilibrium flux periodicity depends on the anyon type and their statistical parameters.

Abstract

We consider the external magnetic field effects on the two types of anyon with fractional statistical parameters $p/q$ with coprimes $p$ and $q$, one with fractional charge $e/q $ and flux $p \phi_0(=hc/e)$(type I), the other with fractional flux $p \phi_0/q$ and fundamental charge $e$(type II). These two-types of anyons show different behaviors in the presence of the external magnetic field. We also considered the geometry in which a two-dimensional plane contains an island of anyons with different statistical parameter in their equilibrium. The equilibrium inside an island is shown to be periodic with respect to the flux through the island. The period for the type I anyon equals to the integer multiple of the fundamental flux quantum. In the case of type II anyon the period is found to be the fractional multiple of the fundamental flux quantum.