String order parameters for symmetry fractionalization in an enriched toric code

We study a simple model of symmetry-enriched topological order obtained by decorating a toric code model with lower-dimensional symmetry-protected topological states. We show that the symmetry fractionalization in this model can be characterized by string order parameters, and that these signatures...

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Bibliographic Details
Published in:Physical review. B 2021-03, Vol.103 (12), p.1, Article 125104
Main Authors: Garre-Rubio, José, Iqbal, Mohsin, Stephen, David T.
Format: Article
Language:English
Subjects:
Mathematical models
Order parameters
Phase diagrams
Phase transitions
Strings
Symmetry
Symmetry detection
Tensors
Topology
Transition points
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Summary:We study a simple model of symmetry-enriched topological order obtained by decorating a toric code model with lower-dimensional symmetry-protected topological states. We show that the symmetry fractionalization in this model can be characterized by string order parameters, and that these signatures are robust under the effects of external fields and interactions, up to the phase transition point. This extends the recent proposal of Garre-Rubio and Iblisdir [New J. Phys. 21, 113016 (2019)] beyond the setting of fixed-point tensor network states, and solidifies string order parameters as a useful tool to characterize and detect symmetry fractionalization. In addition to this, we observe how the condensation of an anyon that fractionalizes a symmetry forces that symmetry to spontaneously break, and we give a proof of this in the framework of projected entangled pair states. This phenomenon leads to a notable change in the phase diagram of the toric code in parallel magnetic fields
ISSN:2469-9950
2469-9969
DOI:10.1103/PhysRevB.103.125104