期刊
PHYSICAL REVIEW B
卷 94, 期 12, 页码 -出版社
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.94.125103
关键词
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资金
- Simons Investigator Award [ONR-N00014-14-1-0330]
- ARO MURI [W911NF-12-1-0461]
- NSF-MRSEC [DMR-1420541]
- Packard Foundation
- Keck grant
- Ministry of Science and Technology of China [2016YFA0302400, 2016YFA0300600]
- Princeton Global Scholarship
- NSF [CAREER ECCS-1351871]
- Office of Naval Research [N0014-11-1-0123]
- DARPA under SPAWAR [N66001-11-1-4110]
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.
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