|As Contributors:||David Tong|
|Submitted by:||Tong, David|
|Submitted to:||SciPost Physics|
|Subject area:||Mathematical Physics|
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.
We thank the referee for their comments.
The referee raises an interesting question: what fraction of the states in the system are under analytic control? Unfortunately this appears to be a rather difficult problem and we do not have the general solution. Indeed, even for seemingly simple cases, like 3 anyons in SU(2), it is complicated.
In an attempt to improve the paper along the lines suggested by the referee, we have included a plot of the low lying states of two SU(2) anyons, in which we include both analytic and non-analytic states. We have elaborated on the difficulty in counting the analytic states in general.
The changes are all on page 21. The referee requested a plot of analytic states for 3 anyons to match that in the introduction. While this plot is simple to construct, we felt that it didn't add much without knowing the non-analytic states as well. This is why we plumped for two anyons instead.