The Pfaffian quantum Hall state made simple--multiple vacua and domain walls on a thin torus

Details The Pfaffian quantum Hall state made simple--multiple vacua and domain walls on a thin torus The Pfaffian quantum Hall state made simple--multiple vacua and domain walls on a thin torus

2006-04-10

arxiv.org/abs/cond-mat/0604251v2

Phys. Rev. B 74, 081308(R) (2006)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

4 pages, 1 figure. Published, minor changes

Scientific paper

10.1103/PhysRevB.74.081308

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 $2^{n-1}$ for $2n-k$ holes and $k$ particles at fixed positions and assign each a charge $\pm e/4$. 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.

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