Pfaffian quantum Hall state made simple: Multiple vacua and domain walls on a thin torus
2006 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 74, no 8, 081308- p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2006. Vol. 74, no 8, 081308- p.
Research subject Theoretical Physics
IdentifiersURN: urn:nbn:se:su:diva-24938DOI: 10.1103/PhysRevB.74.081308ISI: 000240238900011OAI: oai:DiVA.org:su-24938DiVA: diva2:198556