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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 | |
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| Preprint Link: | https://arxiv.org/abs/1611.05848v1 (pdf) |
| Date submitted: | Feb. 6, 2017, 1 a.m. |
| Submitted by: | Tong, David |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
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.
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Reports on this Submission
Strengths
- The authors make a clear connection with the abelian three-anyon problem
- The introduction is well written
- Quantum mechanical conformal invariance is well-explained
- The authors use this invariance to determine the spectrum of non-abelian anyons
- As an alternative, they use perturbation theory to determine the spectrum of some of the states
Weaknesses
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The authors should include a plot like figure 1 to illustrate the difference between abelian and non abelian anyons. It would be nice to see which states can be calculated analytically and which ones are not.
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It is not clear which fraction of the states are accessible analytically. Could the authors comment on that?
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Requested changes
- Add a figure as Fig. 1 for the case of three nonabelian anyons (with only the analytical states).
- Explain how the nonabelian action affects the number of states that can be obtained analytically.