An exactly solvable model for anyons with non-Abelian flux

TL;DR

This paper introduces an exactly solvable two-dimensional model demonstrating how synthetic non-Abelian flux can give rise to anyons with non-Abelian statistics, bridging the gap between Abelian and fully non-Abelian anyons.

Contribution

The authors develop a solvable model for non-Abelian anyons in a 2D electron gas with specific spin interactions and gauge potentials, providing new insights into non-Abelian anyon dynamics.

Findings

Ground state degeneracy due to spin alignment

Adiabatic braiding of solenoids exhibits non-Abelian anyon behavior

Model serves as an intermediate case between Abelian and non-Abelian anyons

Abstract

We present an exactly solvable model for synthetic anyons carrying non-Abelian flux. The model corresponds to a two-dimensional electron gas in a magnetic field with a specific spin interaction term, which allows only fully aligned spin states in the ground state; the ground state subspace is thus two-fold degenerate. This system is perturbed with identical solenoids carrying a non-Abelian gauge potential. We explore dynamics of the ground state as these solenoids are adiabatically braided and show they behave as anyons with a non-Abelian flux. Such a system represents a middle ground between the ordinary Abelian anyons and the fully non-Abelian anyons.