Abstract

We analyze the Moore-Read Pfaffian state on a thin torus. The known six-fold\ndegeneracy is realized by two inequivalent crystalline states with a four- and\ntwo-fold degeneracy respectively. The fundamental quasihole and quasiparticle\nexcitations are domain walls between these vacua, and simple counting arguments\ngive a Hilbert space of dimension $2^{n-1}$ for $2n-k$ holes and $k$ particles\nat fixed positions and assign each a charge $\\pm e/4$. This generalizes the\nknown properties of the hole excitations in the Pfaffian state as deduced using\nconformal field theory techniques. Numerical calculations using a model\nhamiltonian and a small number of particles supports the presence of a stable\nphase with degenerate vacua and quarter charged domain walls also away from the\nthin torus limit. A spin chain hamiltonian encodes the degenerate vacua and the\nvarious domain walls.\n

Keywords

PfaffianTorusQuantum Hall effectSimple (philosophy)State (computer science)PhysicsDomain (mathematical analysis)Fractional quantum Hall effectQuantum mechanicsQuantum spin Hall effectTheoretical physicsMathematicsPure mathematicsGeometryMathematical analysisElectronPhilosophyAlgorithm

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Year
2006
Type
article
Volume
74
Issue
8
Citations
86
Access
Closed

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Emil J. Bergholtz, Janik Kailasvuori, Emma Wikberg et al. (2006). Pfaffian quantum Hall state made simple: Multiple vacua and domain walls on a thin torus. Physical Review B , 74 (8) . https://doi.org/10.1103/physrevb.74.081308

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DOI
10.1103/physrevb.74.081308