We analyze the Moore-Read Pfaffian state on a thin torus. The known six-fold degeneracy is realized by two inequivalent crystalline states with a four- and two-fold 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 supports 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.
@article{arxiv.cond-mat/0604251,
title = {The Pfaffian quantum Hall state made simple--multiple vacua and domain walls on a thin torus},
author = {E. J. Bergholtz and J. Kailasvuori and E. Wikberg and T. H. Hansson and A. Karlhede},
journal= {arXiv preprint arXiv:cond-mat/0604251},
year = {2007}
}