English

Spin Topological Field Theory and Fermionic Matrix Product States

Strongly Correlated Electrons 2018-09-12 v2 High Energy Physics - Theory Mathematical Physics math.MP

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.

Keywords

Cite

@article{arxiv.1610.10075,
  title  = {Spin Topological Field Theory and Fermionic Matrix Product States},
  author = {Anton Kapustin and Alex Turzillo and Minyoung You},
  journal= {arXiv preprint arXiv:1610.10075},
  year   = {2018}
}
R2 v1 2026-06-22T16:37:57.309Z