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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.

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Caltech Authors  


Turzillo, Alex -  You, Minyoung - 

Id.: 71027676

Versión: 1.0

Estado: Final

Tipo:  application/pdf - 

Tipo de recurso: Report or Paper  -  PeerReviewed  - 

Tipo de Interactividad: Expositivo

Nivel de Interactividad: muy bajo

Audiencia: Estudiante  -  Profesor  -  Autor  - 

Estructura: Atomic

Coste: no

Copyright: sí

Formatos:  application/pdf - 

Requerimientos técnicos:  Browser: Any - 

Relación: [References] http://resolver.caltech.edu/CaltechAUTHORS:20180220-094544061
[References] https://authors.library.caltech.edu/84889/

Fecha de contribución: 23-feb-2018


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

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