Average Field Approximation for Almost Bosonic Anyons in a Magnetic Field

TL;DR

This paper investigates the ground state behavior of a large number of 2D anyons in a magnetic field, showing that under certain scaling limits, particles behave like independent bosons with a self-consistent magnetic field.

Contribution

It introduces a novel scaling limit for almost bosonic anyons and rigorously justifies the average field approximation using an information theoretic de Finetti theorem.

Findings

Particles behave like independent bosons in the limit

The average field approximation is rigorously justified

The method handles long-range magnetic interactions

Abstract

We study the ground state of a large number N of 2D anyons in an external magnetic field. We consider a scaling limit where the statistics parameter $\alpha$ tends to zero when N tends to infinity which allows the statistics to be seen as a "perturbation from the bosonic end". Our model is that of bosons in a magnetic field and interacting through long-range magnetic potential generated by magnetic charges carried by each particle, smeared over discs of radius R. Our method allows to take R tends to not too fast at the same time as N tends to infinity. We use the information theoretic version of the de Finetti theorem of Brand{\~a}o and Harrow to justify the so-called "average field approximation": the particles behave like independent, identically distributed bosons interacting via a self-consistent magnetic field.