Computing data for Levin-Wen with defects

Jacob C. Bridgeman1 and Daniel Barter2

1Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada
2Mathematical Sciences Institute, Australian National University, Canberra, Australia

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Abstract

We demonstrate how to do many computations for doubled topological phases with defects. These defects may be 1-dimensional domain walls or 0-dimensional point defects.
Using $\operatorname{Vec}(S_3)$ as a guiding example, we demonstrate how domain wall fusion and associators can be computed using generalized tube algebra techniques. These domain walls can be both between distinct or identical phases. Additionally, we show how to compute all possible point defects, and the fusion and associator data of these. Worked examples, tabulated data and Mathematica code are provided.

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Cited by

[1] Jacob C. Bridgeman, Alexander Hahn, Tobias J. Osborne, and Ramona Wolf, "Gauging defects in quantum spin systems: A case study", Physical Review B 101 13, 134111 (2020).

[2] Alex Bullivant and Clement Delcamp, "Gapped boundaries and string-like excitations in (3+1)d gauge models of topological phases", arXiv:2006.06536.

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