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

Abstract

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.

6 pages, 4 figures

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Cited by in corpus (6)

• Self-dual $S_3$-invariant quantum chains
• Exact dimer phase with anisotropic interaction for one dimensional magnets
• An exact local mapping from clock-spins to fermions
• Noninteracting tight-binding models for Fock parafermions
• Phase diagram of an extended parafermion chain
• Emergent Haldane phase in an alternating bond ${\mathbb{Z}}_3$ parafermion chain