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SUMMARY:Extracting the full anyon data from Kitaev’s Quantum Double mode
 l - Siddharth Vadnerkar\, University of California Davis
DTSTART:20240808T131500Z
DTEND:20240808T141500Z
UID:TALK219832@talks.cam.ac.uk
CONTACT:Laurens Lootens
DESCRIPTION:When studying gapped topological phases\, there are two broad 
 approaches that exist in the literature. One may either study macroscopic 
 anyon data by looking at their Braided Tensor Category (BTC). Alternativel
 y\, one may investigate microscopic models like the Toric Code that demons
 trate topological phenomena. A natural question is to ask if it is possibl
 e to extract anyon data from the microscopic lattice models and organise t
 hem into the nice form of a BTC. Kitaev’s Quantum Double Models (QDM) ar
 e a celebrated class of lattice models that demonstrate important topologi
 cal phenomena like anyons. We answer the above question in the context of 
 QDM\, proving a longstanding conjecture in our setting and concluding that
  Kitaev was right (yet again…)\n\nOur approach is the following. We star
 t with Kitaev’s Quantum Double Model (QDM) in the infinite volume. Using
  a selection criterion\, we pick out ‘anyon sectors’ that roughly desc
 ribe global anyon types. We work out that there are finitely many global a
 nyon types\, each uniquely labelled by the irreducible representations of 
 $D(G)$\, the Quantum Double algebra. We then show these anyon sectors form
  a Braided Tensor Category. Moreover\, this category is braided monoidal e
 quivalent to $Rep(D(G))$\, the category of representations of $D(G)$. Thus
  it is possible to extract all the macroscopic anyon data from the QDM\, i
 ncluding F/R symbols\, by studying the much simpler category\, $Rep(D(G))$
 \, whose anyon data is already known in the literature.\n\nThis talk is ba
 sed on a joint work with Alex Bols (arXiv:2310.19661) and its sequel with 
 Alex Bols\, Mahdie Hamdan\, Pieter Naaijkens (work in progress).
LOCATION:MR9
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