State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter
By Lakshya Bhardwaj, D. Gaiotto, A. Kapustin. 2016
133 citations recorded by the source corpus.
A bstractIt is possible to describe fermionic phases of matter and spin-topological field theories in 2+1d in terms of bosonic “shadow” theories, which are obtained from the original theory by “gauging fermionic parity”. The fermionic/spin theories are recovered from their shadow by a process of fermionic anyon condensation: gauging a one-form symmetry generated by quasi-particles with fermionic statistics. We apply the formalism to theories which admit gapped boundary conditions. We obtain Turaev-Viro-like and Levin-Wen-like constructions of fermionic phases of matter. We describe the group structure of fermionic SPT phases protected by ℤ2f × G. The quaternion group makes a surprise appearance.
Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics
View Paper: https://www.semanticscholar.org/paper/4a12b5953b585a4cd4b69cb60005f412b3c7be33
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In Atomic and Molecular Physics, and Optics
In Condensed Matter Physics
Citations in the corpus
- On 2-group global symmetries and their anomalies (2018, methodology): “Other recent discussions of discrete 2-group symmetry appear in [13–15].”
- Exploring 2-group global symmetries (2018, background): “arlier related work [27,28]. Possible ’t Hooft anomalies for such symmetries were analyzed in [11,29,30]. Other recent discussions of discrete 2-group (and higher n-group) symmetries in QFT appear in [31,16]. Many phenomena that occur for continuous 2-group symmetries also happen in the discrete cas”