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Topological order from parafermions

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If you have a question about this talk, please contact Dr G Moller .

Much effort has been devoted to the study of systems with topological order, motivated by practical issues as well as more field-theoretical and mathematical concerns. A sign of topological order in a gapped one-dimensional quantum chain is the existence of edge zero modes. These occur in the Z_2-invariant Ising/Majorana chain, where they can be understood using free-fermion techniques. Here I show they also occur in strongly interacting spin chains with Z_n symmetry, and are naturally expressed in terms of parafermions. Strikingly, these edge zero modes do not occur in the usual ferromagnetic and antiferromagnetic cases, but rather only when the interactions are chiral, so that spatial-parity and time-reversal symmetries are broken. I will also discuss how some of these ideas can be applied profitably to two-dimensional models.

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