On braid statistics versus parastatistics

Abstract

I report the recent advances in applying (graded) Hopf algebras with braided tensor product in two scenarios: i) paraparticles beyond bosons and fermions living in any space dimensions and transforming under the permutation group; ii) physical models of anyons living in two space-dimensions and transforming under the braid group. In the first scenario simple toy models based on the so-called $2$-bit parastatistics show that, in the multiparticle sector, certain observables can discriminate paraparticles from ordinary bosons/fermions (thus, providing a counterexample to the widespread belief of the "conventionality of parastatistics" argument). In the second scenario the notion of (braided) Majorana qubit is introduced as the simplest building block to implement the Kitaev's proposal of a topological quantum computer which protects from decoherence.

11 pages. Based on a plenary talk at ISQS28, Prague, July 1-5, 2024; to appear in the Proceedings

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• Fault-tolerant quantum computation by anyons
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Cited by in corpus (2)

• An integrable hierarchy associated with loop extension of ${\mathbb{Z}}_2^2$-graded $\mathfrak{osp}(1|2)$
• Parastatistics in Interacting Periodic Chains Revealed by Peierls Phase Twists and Shifted Conformal Towers