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arXiv · 1805.02738

A study of time reversal symmetry of abelian anyons

Yasunori Lee·Yuji Tachikawa
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Abstract

We perform a study of time reversal symmetry of abelian anyons $\mathcal{A}$ in 2+1 dimensions, in the spin structure independent cases. We will find the importance of the group $\mathcal{C}$ of time-reversal-symmetric anyons modulo anyons composed from an anyon and its time reversal. Possible choices of local Kramers degeneracy are given by quadratic refinements of the braiding phases of $\mathcal{C}$, and the anomaly is then given by the Arf invariant of the chosen quadratic refinement. We also give a concrete study of the cases when $|\mathcal{A}|$ is odd or $\mathcal{A}=(\mathbb{Z}_2)^N$.

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Yasunori Lee, Yuji Tachikawa. 2018-05-14. A study of time reversal symmetry of abelian anyons. https://doi.org/10.1007/jhep07(2018)090

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