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Published September 15, 2018 | Published + Submitted
Journal Article Open

Spin Topological Field Theory and Fermionic Matrix Product States

Abstract

We study state-sum constructions of G-equivariant spin topological quantum field theory (TQFTs) and their relationship to matrix product states. In the Neveu-Schwarz, Ramond, and twisted sectors, states of the TQFT are generalized matrix product states. Our results are applied to the classification of fermionic short-range-entangled phases with a unitary symmetry G to 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.

Additional Information

© 2018 American Physical Society. Received 27 February 2018; published 4 September 2018. The research of A.K. was supported by the U. S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and by the Simons Investigator Award.

Attached Files

Published - PhysRevB.98.125101.pdf

Submitted - 1610.10075.pdf

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August 19, 2023
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