Unification of Laughlin and Moore-Read States in SUSY Quantum Hall Effect

Abstract

Based on the recently proposed SUSY quantum Hall effect, we show that Laughlin and Moore-Read states are related by a hidden SUSY transformation. Regarding the SUSY Laughlin wavefunction as a master wavefunction, Laughlin and Moore-Read states appear as two extreme limits of component wavefunctions. Realizations of topological excitations on Laughlin and Moore-Read states are also discussed in the SUSY formalism. We develop a streographically projected formulation of the SUSY quantum Hall effect. With appropriate interpretation of Grassmann odd coordinates, we illustrate striking analogies between SUSY quantum Hall effect and superfluidity.

5 pages, 1 figure, typos fixed

References in corpus (4)

• Supersymmetric Quantum Hall Effect on Fuzzy Supersphere
• Fuzzy Supersphere and Supermonopole
• Quantum Hall Liquid on a Noncommutative Superplane
• Supersymmetric Chern-Simons Theory and Supersymmetric Quantum Hall Liquid

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• SUSY Quantum Hall Effect on Non-Anti-Commutative Geometry
• Free and Interacting Fermionic Conformal Field Theories on the Fuzzy Sphere
• Engineering of Anyons on M5-Probes via Flux Quantization
• Supersymmetric Hamiltonian Approach to Edge Excitations in $\nu =5/2$ Fractional Quantum Hall Effect
• Supersymmetric Quantum Hall Liquid with a Deformed Supersymmetry