Induced Edge States and Domain Walls in the Fractional Quantum Hall Effect Spin Transition

Search for parafermions and Fibonacci anyons, which are excitations obeying non-Abelian statistics, is driven both by the quest for deeper understanding of nature and prospects for universal topological quantum computation. However, physical systems that can host these exotic excitations are rare and hard to realize in experiments. Here we study the domain walls and the edge states formed in spin transitions in the fractional quantum Hall regime. Exact diagonalization of the Hamiltonian in a disk and torus geometries proves the existence of the counter-propagating edge modes with different spin polarizations on the boundaries between areas of the electron liquid in different phase states. We argue that these systems may host parafermions when coupled to an s-wave superconductor and are experimentally feasible.