Topological Insulating Phases of Non-Abelian Anyonic Chains

Abstract

Boundary conformal field theory is brought to bear on the study of topological insulating phases of non-abelian anyonic chains. These topologically non-trivial phases display protected anyonic end modes. We consider antiferromagnetically coupled spin-1/2 su(2)${}_k$ chains at any level $k$, focusing on the most prominent examples; the case $k=2$ describes Ising anyons (equivalent to Majorana fermions) and $k=3$ corresponds to Fibonacci anyons. We prove that the braiding of these emergent anyons exhibits the same braiding behavior as the physical quasiparticles. These results suggest a `solid-state' topological quantum computation scheme in which the emergent anyons are braided by simply tuning couplings of non-Abelian quasiparticles in a fixed network.

arXiv comment5 pages, 3 figures, 1 table

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Cited by in corpus (5)

• One-Dimensional Symmetry Protected Topological Phases and their Transitions
• Relationship between Symmetry Protected Topological Phases and Boundary Conformal Field Theories via the Entanglement Spectrum
• Anyonic Haldane insulator in one dimension
• Characterizing the Entanglement of Anyonic Systems using the Anyonic Partial Transpose
• Phases of Interacting Fibonacci Anyons on a Ladder at Half-Filling