The Conformal Spectrum of Non-Abelian Anyons

TL;DR

This paper investigates the energy spectrum of non-Abelian anyons in a harmonic trap, revealing how their angular momentum and protected states are governed by conformal symmetry and algebraic properties.

Contribution

It provides a detailed analysis of the spectrum of non-Abelian anyons using Chern-Simons theory, highlighting the role of conformal invariance and quadratic Casimirs in determining bound state properties.

Findings

Angular momentum of bound states is determined by quadratic Casimirs.

Identification of protected states with energies dictated by angular momentum.

Spectrum exhibits special properties due to conformal invariance.

Abstract

We study the spectrum of multiple non-Abelian anyons in a harmonic trap. The system is described by Chern-Simons theory, coupled to either bosonic or fermionic non-relativistic matter, and has an SO(2,1) conformal invariance. We describe a number of special properties of the spectrum, focussing on a class of protected states whose energies are dictated by their angular momentum. We show that the angular momentum of a bound state of non-Abelian anyons is determined by the quadratic Casimirs of their constituents.