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Kosaki-Longo index and classification of charges in 2D quantum spin models

Naaijkens, Pieter ORCID: 2013. Kosaki-Longo index and classification of charges in 2D quantum spin models. Journal of Mathematical Physics 54 (8) , 081901. 10.1063/1.4818272

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We consider charge superselection sectors of two-dimensional quantum spin models corresponding to cone localisable charges, and prove that the number of equivalence classes of such charges is bounded by the Kosaki-Longo index of an inclusion of certain observable algebras. To demonstrate the power of this result we apply the theory to the toric code on a 2D infinite lattice. For this model we can compute the index of this inclusion, and conclude that there are four distinct irreducible charges in this model, in accordance with the analysis of the toric code model on compact surfaces. We also give a sufficient criterion for the non-degeneracy of the charge sectors, in the sense that Verlinde's matrix S is invertible.

Item Type: Article
Status: Published
Schools: Mathematics
Publisher: American Institute of Physics (AIP)
ISSN: 0022-2488
Last Modified: 07 Nov 2022 09:35

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