2006/04/30 by E. J. Bergholtz, Emil J. Bergholtz, Janik Kailasvuori +5 · 2 citations
Computer Science · Physics and Astronomy · #Quantum Information and Cryptography #Quantum and electron transport phenomena #Quantum-Dot Cellular Automata #cond-mat.mes-hall #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.74.081308
published as Phys. Rev. B 74, 081308(R) (2006) · 4 pages, 1 figure. Published, minor changes
openalex publication_date 2006/08/31 · arxiv created 2006/09/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 2^n\ensuremath-1 for 2n\ensuremath-k holes and k particles at fixed positions and assign each a charge \ifmmode±\else\textpm\fie∕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.