Topological phase, supercritical point and emergent phenomena in extended \(\mathbb{Z}_3\) parafermion chain

Topological orders and associated topological protected excitations satisfying non-Abelian statistics have been widely explored in various platforms. The \(\mathbb{Z}_3\) parafermions are regarded as the most natural generation of the Majorana fermions to realize these topological orders. Here we in...

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Bibliographic Details
Published in:arXiv.org 2018-03
Main Authors: Shun-Yao, Zhang, Hong-Ze Xu, Yue-Xin, Huang, Guo, Guang-Can, Zheng-Wei, Zhou, Gong, Ming
Format: Article
Language:English
Subjects:
Chains
Dimers
Excitation
Fermions
Ferromagnetic phases
Ferromagnetism
Phase diagrams
Topology
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Summary:Topological orders and associated topological protected excitations satisfying non-Abelian statistics have been widely explored in various platforms. The \(\mathbb{Z}_3\) parafermions are regarded as the most natural generation of the Majorana fermions to realize these topological orders. Here we investigate the topological phase and emergent \(\mathbb{Z}_2\) spin phases in an extended parafermion chain. This model exhibits rich variety of phases, including not only topological ferromagnetic phase, which supports non-Abelian anyon excitation, but also spin-fluid, dimer and chiral phases from the emergent \(\mathbb{Z}_2\) spin model. We generalize the measurement tools in \(\mathbb{Z}_2\) spin models to fully characterize these phases in the extended parafermion model and map out the corresponding phase diagram. Surprisingly, we find that all the phase boundaries finally merge to a single supercritical point. In regarding of the rather generality of emergent phenomena in parafermion models, this approach opens a wide range of intriguing applications in investigating the exotic phases in other parafermion models.
ISSN:2331-8422
DOI:10.48550/arxiv.1801.03269