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arXiv · 1407.2994

Anyon and Loop Braiding Statistics in Field Theories with a Topological $\Theta-$term

Zhen Bi·Yi-Zhuang You·Cenke Xu
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Abstract

We demonstrate that the anyon statistics and three-loop statistics of various 2d and 3d topological phases can be derived using semiclassical nonlinear Sigma model field theories with a topological $\Theta$-term. In our formalism, the braiding statistics has a natural geometric meaning: The braiding process of anyons or loops leads to a nontrivial field configuration in the space-time, which will contribute a braiding phase factor due to the $\Theta$-term.

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Zhen Bi, Yi-Zhuang You, Cenke Xu. 2014-07-11. Anyon and Loop Braiding Statistics in Field Theories with a Topological $\Theta-$term. https://doi.org/10.1103/physrevb.90.081110

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