Exact Hamiltonian for non-Abelian quasiparticle states

Non-Abelian anyons have been predicted to emerge in the 5/2 fractional quantum Hall effect. Here, we propose a model Hamiltonian that is exactly solvable for non-Abelian quasiparticles (QPs) as well as quasiholes (QHs). Motivated by the bipartite composite fermion theory [1,2], we construct interactions in terms of two- and three-body Haldane's pseudopotentials. The QP and QH states exhibit the same counting for edge excitations, implying that they obey the same non-Abelian statistics. Our model provides exact solutions for neutral excitations as well. We demonstrate adiabatic continuity for the neutral excited states as we deform our Hamiltonian into the lowest Landau level Hamiltonian with a three-body interaction.

[1] G. J. Sreejith, C. Töke, A. Wójs, and J. K. Jain, Phys. Rev. Lett. 107, 086806 (2011)

[2] I. D. Rodriguez, A. Sterdyniak, M. Hermanns, J. K. Slingerland, and N. Regnault, Phys. Rev. B 85, 035128 (2012)