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Fermionic Matrix Product States and One-Dimensional Short-Range Entangled Phases with Anti-Unitary Symmetries

Turzillo, Alex and You, Minyoung (2017) Fermionic Matrix Product States and One-Dimensional Short-Range Entangled Phases with Anti-Unitary Symmetries. . (Submitted) https://resolver.caltech.edu/CaltechAUTHORS:20180220-094544061

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Abstract

We extend the formalism ofMatrix Product States (MPS) to describe one-dimensional gapped systems of fermions with both unitary and anti-unitary 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 an RG 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 non-trivial extensions of fermion parity and time-reversal.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
https://arxiv.org/abs/1710.00140arXivDiscussion Paper
ORCID:
AuthorORCID
Turzillo, Alex0000-0003-4293-4293
Additional Information:Submitted on 30 Sep 2017. 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 Number de-sc0011632.
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
Record Number:CaltechAUTHORS:20180220-094544061
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20180220-094544061
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:84889
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:22 Feb 2018 04:39
Last Modified:03 Oct 2019 19:24

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