Parafermions in Hierarchical Fractional Quantum Hall States

Non-Abelian quasiparticles are sought-after building blocks of fault-tolerant quantum computation. These quasiparticles can occur as extrinsic defects on interfaces and edges of two-dimensional Abelian topological phases, of which the Fractional quantum Hall (FQH) effect provides the most abundant realization. In this talk, we will discuss the properties of parafermion zero modes that arise as extrinsic non-Abelian defects in domain walls formed on interfaces of hierarchical FQH Jain states with filling fraction p/(2mp+1) of the lowest Landau level, where m and p are positive integers. Exploring the condensation of bulk Abelian anyons, we use Abelian bosonization to construct local interactions that gap modes with opposite chirality at the interface of two Jain states with the same filling fraction. We identify a class of such local interactions that breaks charge conservation and gives rise to an interface anyon condensate supporting parafermion zero modes whose quantum dimension reflects the topological order and the hierarchy of the bulk FQH Jain state. Our results shed light on the hierarchy of non-Abelian defects in two-dimensional Abelian topological phases. Reference: arXiv:1906.07188