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

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Velenich, Andrea
Chamon, Claudio
Wen, Xiao-Gang
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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.
Comment: 4 pages
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Condensed Matter - Strongly Correlated Electrons
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