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- Bergholtz, E. J., et al.
(author)
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Pfaffian quantum Hall state made simple : Multiple vacua and domain walls on a thin torus
- 2006
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In: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 74:8, s. 081308-
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Journal article (peer-reviewed)abstract
- 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.
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