Topological phases with parafermions: theory and blueprints
Annual Review of Condensed Matter Physics Annual Reviews 7:1 (2016) 119-139
Abstract:
We concisely review the recent evolution in the study of parafermions—exotic emergent excitations that generalize Majorana fermions and similarly underpin a host of novel phenomena. First we generalize the intimate connection between the -symmetric Ising quantum spin chain and Majorana fermions to -symmetric chains and parafermions. In particular, we highlight how parafermion chains host a topological phase featuring protected edge zero modes. We then tour several blueprints for the laboratory realization of parafermion zero modes—focusing on quantum Hall/superconductor hybrids, quantum Hall bilayers, and two-dimensional topological insulators—and describe striking experimental fingerprints that they provide. Finally, we discuss how coupled parafermion arrays in quantum Hall architectures yield topological phases that potentially furnish hardware for a universal, intrinsically decoherence-free quantum computer.Parafermionic conformal field theory on the lattice
Journal of Physics A: Mathematical and Theoretical IOP Publishing 47:45 (2014) 452001
Stability of zero modes in parafermion chains
Physical Review B American Physical Society (APS) 90:16 (2014) 165106
Corner contribution to the entanglement entropy of an O(3) quantum critical point in 2 + 1 dimensions
Journal of Statistical Mechanics Theory and Experiment IOP Publishing 2014:6 (2014) p06009
Geometric mutual information at classical critical points.
Physical review letters 112:12 (2014) 127204