Spin-flux attachment by dimensional reduction of vortices

TL;DR

This paper explores how vortices in a 2+1-dimensional system can be attached to fermions via their magnetic moments, leading to fractional statistics similar to anyons, without relying on Chern-Simons theory.

Contribution

It demonstrates a novel mechanism for flux attachment and anyon-like behavior in 2+1 dimensions through vortex-fermion interactions derived from dualizing higher-dimensional systems.

Findings

Vortices are attached to fermions via their magnetic moments.

Particles exhibit fractional statistics akin to anyons.

The model realizes anyons without Chern-Simons gauge theory.

Abstract

The description of a system of vortices in terms of dual fields provides a window to new phases of the system. It was found recently that dualizing a 3+1-d boson-fermion system leads to a system of fermions and vortices interacting via a 2-form field through a non-local term. Here we explore some consequences of such an interaction when the degrees of freedom of the system are confined to a 2+1-d space-time. In particular, we show that the vortices in the 2+1-d system are attached to the fermions via their non-zero spin magnetic moment in a way similar to the phenomenon of flux attachment in Chern-Simons gauge theory coupled to matter. We also show that such flux attached particles exhibit fractional statistical behaviour like anyons. Thus our model provides a realization of anyons without Chern-Simons theory.