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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.

Published as SciPost Phys. 4, 022 (2018)

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.

Submission & Refereeing History

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Resubmission 1611.05848v2 on 7 March 2018

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