String-nets, single and double-stranded quantum loop gases for non-Abelian anyons

Details String-nets, single and double-stranded quantum loop gases for non-Abelian anyons String-nets, single and double-stranded quantum loop gases for non-Abelian anyons

2009-11-05

arxiv.org/abs/0911.1132v1

J.Phys.A43:172002,2010

Physics

Condensed Matter

Strongly Correlated Electrons

4 pages

Scientific paper

10.1088/1751-8113/43/17/172002

String-net condensation can give rise to non-Abelian anyons whereas loop condensation usually gives rise to Abelian anyons. It has been proposed that generalized quantum loop gases with non-orthogonal inner products can produce non-Abelian anyons. We detail an exact mapping between the string-net and the generalized loop models and explain how the non-orthogonal products arise. We also introduce a loop model of double-stranded nets where quantum loops with an orthogonal inner product and local interactions supports non-Abelian Fibonacci anyons. Finally we emphasize the origin of the sign problem in such systems and its consequences on the complexity of their ground state wave functions.

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