Universal properties of anyon braiding on one-dimensional wire networks

Abstract

We demonstrate that anyons on wire networks have fundamentally different braiding properties than anyons in 2D. Our analysis reveals an unexpectedly wide variety of possible non-abelian braiding behaviours on networks. The character of braiding depends on the topological invariant called the connectedness of the network. As one of our most striking consequences, particles on modular networks can change their statistical properties when moving between different modules. However, sufficiently highly connected networks already reproduce braiding properties of 2D systems. Our analysis is fully topological and independent on the physical model of anyons.

6 pages, a companion paper to arXiv:2006.15256

References in corpus (5)

• Non-Abelian Anyons and Topological Quantum Computation
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
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Cited by in corpus (5)

• Parafermions in a multilegged geometry: Towards a scalable parafermionic network
• A Generalization of the One-Dimensional Boson-Fermion Duality Through the Path-Integral Formalism
• Quantum Walk on Orbit Spaces
• Compatibility of Braiding and Fusion on Wire Networks
• Extending the planar theory of anyons to quantum wire networks