dc.contributor.author | Cowtan, A | |
dc.contributor.author | Majid, S | |
dc.date.accessioned | 2023-11-28T15:21:03Z | |
dc.date.available | 2023-11-28T15:21:03Z | |
dc.date.issued | 2022-08-12 | |
dc.identifier.uri | https://qmro.qmul.ac.uk/xmlui/handle/123456789/92346 | |
dc.description.abstract | We provide a systematic treatment of boundaries based on subgroups K ⊆ G for the Kitaev quantum double D(G) model in the bulk. The boundary sites are representations of a
-subalgebra Ξ ⊆ D(G) and we explicate its structure as a quasi-Hopf
-algebra dependent on a choice of transversal R. We provide decomposition formulae for irreducible representations of D(G) pulled back to Ξ. As an application of our treatment, we study patches with boundaries based on K = G horizontally and K = {e} vertically and show how these could be used in a quantum computer using the technique of lattice surgery. More abstractly, we also provide explicitly the monoidal equivalence of the category of Ξ-modules and the category of G-graded K-bimodules and use this to prove that different choices of R are related by Drinfeld cochain twists. Examples include Sn−1 ⊂ Sn and an example related to the octonions where Ξ is also a Hopf quasigroup. | en_US |
dc.publisher | AIP Publishing | en_US |
dc.rights | All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). | |
dc.rights | Attribution 3.0 United States | * |
dc.rights.uri | http://creativecommons.org/licenses/by/3.0/us/ | * |
dc.subject | quant-ph | en_US |
dc.subject | quant-ph | en_US |
dc.subject | math-ph | en_US |
dc.subject | math.MP | en_US |
dc.subject | math.QA | en_US |
dc.title | Algebraic Aspects of Boundaries in the Kitaev Quantum Double Model | en_US |
dc.rights.holder | © 2023 Author(s). | |
pubs.author-url | http://arxiv.org/abs/2208.06317v1 | en_US |
pubs.notes | Not known | en_US |
rioxxterms.funder | Default funder | en_US |
rioxxterms.identifier.project | Default project | en_US |