Topological phases with parafermions: theory and blueprints by Alicea, J, Fendley, P

“…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. …”

Exotic phases of interacting Majorana fermions and parafermions by O'Brien, E

“…<p>In this thesis exotic phases of models preserving the symmetries of the one-dimensional quantum Ising and three-state Potts chains are considered, the natural habitats of Majorana fermions and parafermions, respectively. Along with numerical techniques, conformal field theory (CFT) is used to study the resulting physics.…”

Prethermal strong zero modes and topological qubits by Else, D, Fendley, P, Kemp, J, Nayak, C

“…We analyze the ramifications for ordered and topological phases in one, two, and three dimensions, with examples including Majorana and parafermionic zero modes in interacting spin chains. …”

"Not-A", representation symmetry-protected topological, and Potts phases in an S-3-invariant chain by O'Brien, E, Vernier, E, Fendley, P

“…One has three-state Potts order, corresponding to topological order in a parafermionic formulation. Another has “representation” symmetry-protected topological (RSPT) order, while its dual exhibits an unusual “not- A ” order, where the spins prefer to align in two of the three directions. …”

“Not- A”, representation symmetry-protected topological, and Potts phases in an S3 -invariant chain by O’Brien. E, Vernier, E, Fendley, P

“…One has three-state Potts order, corresponding to topological order in a parafermionic formulation. Another has “representation” symmetry-protected topological (RSPT) order, while its dual exhibits an unusual “not- A ” order, where the spins prefer to align in two of the three directions. …”