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Fermionic matrix product states and one-dimensional short-range entangled phases with antiunitary symmetries

Turzillo, Alex and You, Minyoung (2019) Fermionic matrix product states and one-dimensional short-range entangled phases with antiunitary symmetries. Physical Review B, 99 (3). Art. No. 035103. ISSN 2469-9950. doi:10.1103/physrevb.99.035103.

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We extend the formalism of matrix product states (MPS) to describe one-dimensional gapped systems of fermions with both unitary and antiunitary symmetries. Additionally, systems with orientation-reversing spatial symmetries are considered. The short-ranged entangled phases of such systems are classified by three invariants, which characterize the projective action of the symmetry on edge states. We give interpretations of these invariants as properties of states on the closed chain. The relationship between fermionic MPS systems at a renormalization group fixed point and equivariant algebras is exploited to derive a group law for the stacking of fermionic phases. The result generalizes known classifications to symmetry groups that are nontrivial extensions of fermion parity and time-reversal.

Item Type:Article
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Turzillo, Alex0000-0003-4293-4293
Additional Information:© 2019 American Physical Society. (Received 9 August 2018; revised manuscript received 11 December 2018; published 2 January 2019) The authors would like to thank A. Kapustin for helpful discussions throughout the production of this paper. This research was supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632.
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
Issue or Number:3
Record Number:CaltechAUTHORS:20190102-135256710
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:91990
Deposited By: George Porter
Deposited On:03 Jan 2019 15:30
Last Modified:16 Nov 2021 03:46

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