Supersymmetric Quantum Hall Liquid with a Deformed Supersymmetry

Abstract

We construct a supersymmetric quantum Hall liquid with a deformed supersymmetry. One parameter is introduced in the supersymmetric Laughlin wavefunction to realize the original Laughlin wavefunction and the Moore-Read wavefunction in two extremal limits of the parameter. The introduced parameter corresponds to the coherence factor in the BCS theory. It is pointed out that the parameter-dependent supersymmetric Laughlin wavefunction enjoys a deformed supersymmetry. Based on the deformed supersymmetry, we construct a pseudo-potential Hamiltonian whose groundstate is exactly the parameter-dependent supersymmetric Laughlin wavefunction. Though the SUSY pseudo-potential Hamiltonian is parameter-dependent and non-Hermitian, its eigenvalues are parameter-independent and real.

14 pages, contribution to the proceedings of the Group 27 conference, Yerevan, Armenia, August 13-19, 2008, published version

References in corpus (12)

• Making Sense of Non-Hermitian Hamiltonians
• Quantum Hall Effect in Higher Dimensions, Matrix Models and Fuzzy Geometry
• Supersymmetric Quantum Hall Effect on Fuzzy Supersphere
• Fuzzy Supersphere and Supermonopole
• Quantum Hall Effect on Higher Dimensional Spaces
• Quantum Hall Liquid on a Noncommutative Superplane
• Planar Super-Landau Models Revisited
• Planar Super-Landau Models
• Supersymmetrizing Landau Models
• Unitary Spherical Super-Landau Models
• Unification of Laughlin and Moore-Read States in SUSY Quantum Hall Effect
• Supersymmetric Chern-Simons Theory and Supersymmetric Quantum Hall Liquid