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Edge <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="double-struck">Z</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math> parafermions in fermionic lattices
Parafermion modes are non-Abelian anyons which were introduced as ${\mathbb{Z}}_{N}$ generalizations of ${\mathbb{Z}}_{2}$ Majorana states. In particular, ${\mathbb{Z}}_{3}$ parafermions can be used to produce Fibonacci anyons, laying a path towards universal topological quantum computation. Due to their fractional nature, much of the theoretical work on ${\mathbb{Z}}_{3}$ parafermions has relied on …