State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter
Abstract
It 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 the product of fermion parity and internal symmetry G. The quaternion group makes a surprise appearance.
Keywords
Cite
@article{arxiv.1605.01640,
title = {State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter},
author = {Lakshya Bhardwaj and Davide Gaiotto and Anton Kapustin},
journal= {arXiv preprint arXiv:1605.01640},
year = {2017}
}
Comments
92 pages. v2: an analysis of the equivariant toric code in the appendix has been corrected and simplified