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(3+1)-TQFTs and topological insulators

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Abstract

Levin-Wen models are microscopic spin models for topological phases of matter in (2+1)-dimension. We introduce a generalization of such models to (3 + 1)-dimension based on unitary braided fusion categories, also known as unitary premodular categories. We discuss the ground state degeneracy on 3-manifolds and statistics of excitations which include both points and defect loops. Potential connections with recently proposed fractional topological insulators and projective ribbon permutation statistics are described.

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Authors and Affiliations

  1. Microsoft Station Q, CNSI Bldg. Rm. 2243, University of California, Santa Barbara, CA, 93106-6105, USA

    Kevin Walker & Zhenghan Wang

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  1. Kevin Walker
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  2. Zhenghan Wang
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Correspondence to Zhenghan Wang.

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Walker, K., Wang, Z. (3+1)-TQFTs and topological insulators. Front. Phys. 7, 150–159 (2012). https://doi.org/10.1007/s11467-011-0194-z

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  • DOI: https://doi.org/10.1007/s11467-011-0194-z

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