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

TL;DR

This paper explores how string-net and loop gas models can be used to realize non-Abelian anyons, introducing a double-stranded loop model supporting Fibonacci anyons and discussing the implications of the sign problem.

Contribution

It provides an exact mapping between string-net and generalized loop models, and introduces a double-stranded loop model supporting non-Abelian Fibonacci anyons.

Findings

Exact mapping between string-net and loop models.

Double-stranded loop model supports Fibonacci anyons.

Discussion of the sign problem and its impact on ground state complexity.

Abstract

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.