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Parafermionic phases with symmetry breaking and topological order

Author(s): Alexandradinata, A; Regnault, N; Fang, Chen; Gilbert, Matthew J; Bernevig, Bogdan A.

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Abstract: Parafermions are the simplest generalizations of Majorana fermions that realize topological order. We propose a less restrictive notion of topological order in one-dimensional open chains, which generalizes the seminal work by Fendley [J. Stat. Mech. (2012) P11020]. The first essential property is that the ground states are mutually indistinguishable by local, symmetric probes, and the second is a generalized notion of zero edge modes which cyclically permute the ground states. These two properties are shown to be topologically robust, and applicable to a wider family of topologically ordered Hamiltonians than has been previously considered. As an application of these edge modes, we formulate a notion of twisted boundary conditions on a closed chain, which guarantees that the closed-chain ground state is topological, i.e., it originates from the topological manifold of the open chain. Finally, we generalize these ideas to describe symmetry-breaking phases with a parafermionic order parameter. These exotic phases are condensates of parafermion multiplets, which generalize Cooper pairing in superconductors. The stability of these condensates is investigated on both open and closed chains.
Publication Date: 2-Sep-2016
Electronic Publication Date: 2-Sep-2016
Citation: Alexandradinata, A, Regnault, N, Fang, Chen, Gilbert, Matthew J, Bernevig, B Andrei. (2016). Parafermionic phases with symmetry breaking and topological order. PHYSICAL REVIEW B, 94 (10.1103/PhysRevB.94.125103
DOI: doi:10.1103/PhysRevB.94.125103
ISSN: 2469-9950
EISSN: 2469-9969
Type of Material: Journal Article
Journal/Proceeding Title: PHYSICAL REVIEW B
Version: Final published version. Article is made available in OAR by the publisher's permission or policy.

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