Quasielectrons in Abelian and non-Abelian Quantum Hall states

Hans Hansson

Stockholm University, Sweden

We explain a general procedure for constructing quasielectron excitations in quantum Hall states where the wave functions can be expressed in terms of correlators in a conformal field theory. It allows us to construct multi quasielectron states in both Abelian and non-Abelian states, and in particular we obtain explicit wave functions for quasielectrons in the Moore-Read Pfaffian state. By forming coherent states of quasielectrons we can generate a subset of the Haldane-Halperin hierarchy, and in particular obtain an explicit wave function for the observed state at filling factor 4/11. Furthermore, when evaluated on a thin torus or cylinder, all these states coincide with those obtained as an exact solution to a Hamiltonian using a generic repulsive interaction. At a technical level, we introduce a quasilocal operator that creates quasielectrons when inserted in conformal field theory correlators, and we show how to write the states in the positive Jain series on an explicitly hierarchical form.