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The Conformal Spectrum of Non-Abelian Anyons

by Nima Doroud, David Tong, Carl Turner

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Submission summary

Authors (as registered SciPost users): Nima Doroud · David Tong · Carl Turner
Submission information
Preprint Link:  (pdf)
Date accepted: 2018-03-19
Date submitted: 2018-03-07 01:00
Submitted by: Tong, David
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Mathematical Physics
Approach: Theoretical


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.

Author comments upon resubmission

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.

List of changes

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.

Published as SciPost Phys. 4, 022 (2018)

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