Spin topological field theory and fermionic matrix product states
2018
We study state-sum constructions of G-equivariant spin-TQFTs and their relationship to Matrix
Product States. We show that in the Neveu-Schwarz, Ramond, and twisted sectors, the states of the theory
are generalized Matrix Product States. We apply our results to revisit the classification of fermionic
Short-Range-Entangled phases with a unitary symmetry G and determine the group law on the set of
such phases. Interesting subtleties appear when the total symmetry group is a nontrivial extension of G
by fermion parity.
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