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. …”

Discretely holomorphic parafermions and integrable loop models by Ikhlef, Y, Cardy, J

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.…”

Discretely holomorphic parafermions and integrable loop models by Ikhlef, Y, Cardy, J

“…We define parafermionic observables in various lattice loop models, including examples where no Kramers-Wannier duality holds. …”

Holomorphic parafermions in the Potts model and stochastic Loewner evolution by Riva, V, Cardy, J

Discretely holomorphic parafermions in lattice Z(N) models by Rajabpour, M, Cardy, J

Energy transport in an integrable parafermionic chain via generalized hydrodynamics by Mazza, L, Viti, J, Carrega, M, Rossini, D, De Luca, A

“…We study energy transport in the integrable $\mathbb Z_3$ parafermionic chain using the partitioning protocol. …”

How SU(2)4 Anyons are Z3 Parafermions by Fern, R, Kombe, J, Simon, S

“…We show that these braiding properties can be represented exactly using ${Z}_3$ parafermion operators.…”

Generalized quantum Hall projection Hamiltonians by Simon, S, Rezayi, E, Cooper, N

“…Certain well known quantum Hall states-including the Laughlin states, the Moore-Read Pfaffian, and the Read-Rezayi Parafermion states-can be defined as the unique lowest degree symmetric analytic function that vanishes as at least p powers as some number (g+1) of particles approach the same point. …”

Localization-protected order in spin chains with non-Abelian discrete symmetries by Friedman, A, Vasseur, R, Potter, A, Parameswaran, S

“…In a dual formulation, our results indicate the existence of a stable finite-temperature topological phase with MBL-protected parafermionic end zero modes. While we find a thermal symmetry-preserving regime for weak disorder, scaling analysis at strong disorder points to an infinite-randomness critical point between two distinct broken-symmetry MBL phases.…”

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. …”