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arXiv · 1905.02457

Braiding Flux-Tubes in Topological Quantum and Classical Lattice Models from Class-D

Yifei Liu·Yingkai Liu·Emil Prodan
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Abstract

We use magnetic flux-tubes to stabilize zero-energy modes in a lattice realization of a 2-dimensional superconductor from class D of classification table of topological condensed matter systems. The zero modes are exchanged by slowly displacing the flux-tubes and an application of the adiabatic theorem demonstrates the geometric nature of the resulting unitary time-evolution operators. Furthermore, an explicit numerical evaluation reveals that the evolutions are in fact topological, hence supplying a representation of the braid group, which turns out to be non-abelian. This physical representation is further formalized using single-strand planar diagrams. Lastly, we discuss how these predictions can be implemented with and observed in classical meta-materials and how the standard Majorana representation of the braid group can be generated by measuring derived physical observables.

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Yifei Liu, Yingkai Liu, Emil Prodan. 2019-05-14. Braiding Flux-Tubes in Topological Quantum and Classical Lattice Models from Class-D. https://doi.org/10.1016/j.aop.2020.168089

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