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arXiv · 1610.10075

Spin Topological Field Theory and Fermionic Matrix Product States

Anton Kapustin·Alex Turzillo·Minyoung You
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Abstract

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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Anton Kapustin, Alex Turzillo, Minyoung You. 2016-10-31. Spin Topological Field Theory and Fermionic Matrix Product States. https://doi.org/10.1103/physrevb.98.125101

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