Pfaffian quantum Hall state made simple: Multiple vacua and domain walls on a thin torus

Pfaffian quantum Hall state made simple : Multiple vacua and domain walls on a thin torus

We analyze the Moore-Read Pfaffian state on a thin torus. The known sixfold degeneracy is realized by two inequivalent crystalline states with a four- and twofold degeneracy, respectively. The fundamental quasihole and quasiparticle excitations are domain walls between these vacua, and simple counting arguments give a Hilbert space of dimension 2n−1 for 2n−k holes and k particles at fixed positions and assign each a charge ±e∕4. This generalizes the known properties of the hole excitations in the Pfaffian state as deduced using conformal field theory techniques. Numerical calculations using a model Hamiltonian and a small number of particles support the presence of a stable phase with degenerate vacua and quarter-charged domain walls also away from the thin-torus limit. A spin-chain Hamiltonian encodes the degenerate vacua and the various domain walls.

In:Physical Review B. Condensed Matter and Materials Physics74:8, s. 081308-1098-01211550-235X

By the author/editor: Bergholtz, E. J.; Kailasvuori, J.; Wikberg, Emma, 1 ...; Hansson, Thors H ...; Karlhede, Anders

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