Department of Mathematics

Mathematical Physics and Gauge Theory

  •  Stability of superselection sectors in infinite quantum spin systems
  •  09/14/2017
  •  11:00 AM - 12:00 PM
  •  C304 Wells Hall
  •  Matthew Cha, MSU

Superselection sectors are equivalence classes of unitarily equivalent representations and can be used to label charges in a quantum system.  We consider a family of superselection sectors for infinite quantum spin systems corresponding to almost localized endomorphisms. If the vacuum state is pure and satisfies certain locality conditions, we show how to recover the charge statistics. In particular, the superselection structure is that of a braided tensor category, and further, is stable against deformations by a quasi-local dynamics. We apply our results to prove stability of anyons in Kitaev's quantum double.  Braided tensor categories naturally appear as the algebraic theory of anyons in topological phases of matter.  Our results provide evidence that the anyonic structure is an invariant of topologically ordered states.  This is work is joint with Pieter Naaijkens and Bruno Nachtergaele.

 

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Department of Mathematics
Michigan State University
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East Lansing, MI 48824

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