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Open Quantum Systems Decoherence Quantum Simulation Entanglement Theory Quantum Correlations

Anyons and the HOMFLY Skein Algebra

arXiv
Authors: Sachin J. Valera

Year

2018

Paper ID

23629

Status

Preprint

Abstract Read

~2 min

Abstract Words

108

Citations

N/A

Abstract

We give an exposition of how the Kauffman bracket arises for certain systems of anyons, and do so outside the usual arena of Temperley-Lieb-Jones categories. This is further elucidated through the discussion of the Iwahori-Hecke algebra and its relation to modular tensor categories. We then proceed to classify the framed link-invariants associated to a system of self-dual anyons q with sumxNqqxleq2. In particular, we construct a trace on the HOMFLY skein algebra which can be expanded via gauge-invariant quantities, thereby generalising the case of the Kauffman bracket. Various examples are provided, and we deduce some interesting properties of these anyons along the way.

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  • This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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  • We give an exposition of how the Kauffman bracket arises for certain systems of anyons, and do so outside the usual arena of Temperley-Lieb-Jones categories.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1811.01025 [2] arXiv https://arxiv.org/abs/1811.01025 [3] Publisher https://arxiv.org/abs/1811.01025

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